John Christian Ottem

Professor - Algebra, geometri og topologi

$Bilde av John Christian Ottem$

English version of this page

E-post johnco@math.uio.no

Telefon +47 22855930

Rom 1109

Brukernavn

Besøksadresse Moltke Moes vei 35 Niels Henrik Abels hus 0851 Oslo

Postadresse Postboks 1053 Blindern 0316 Oslo

Last ned visittkort

Personal webpage

Research interests

Higher dimensional algebraic geometry, positivity of line bundles and subschemes, Calabi-Yau manifolds, and the moduli space of curves.

Projects

'Young Research Talents'. Research Council of Norway 2016-2021.

Teaching

This term I am teaching MAT1110 - Calculus and linear algebra and MAT4215 - Algebraic Geometry II.

Students

Bernt Ivar Utstøl Nødland (2016-2019)
Bjørn Skauli (2018-)
Martin Helsø (2017-, co-advisor)
Elisa Cazzador (2018-, co-advisor)
Simen Westbye Moe (2019-)

Publications

An O -acyclic variety of even index (with F. Suzuki) (2020)
A refinement of the motivic volume, and specialization of birational types (with J. Nicaise) (2020)
Two coniveau filtrations (with O. Benoist) (2020)
Tropical degenerations and stable rationality (Updated version: Oct 2020) (with J. Nicaise) (2019) Video 1 Video 2 Video 3
A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) Mathematische Annalen 377 (2020), 183–197. Video
On deformations of quintic and septic hypersurfaces (with S. Schreieder) Journal de Mathématiques Pures et Appliquées 135 (2020), 140-158.
Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) Épijournal de Géométrie Algébrique 4 (2020).
Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) Communications in Contemporary Mathematics (2020)
Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). Commentarii Mathematici Helvetici 95 (2020) 27-35.
A counterexample to the birational Torelli problem for Calabi-Yau 3-folds (with J. V. Rennemo). Journal of the London Mathematical Society 97 (2018), 427-440
Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664-695.
Nef cycles on some hyperkahler fourfolds. Facets of Algebraic Geometry: A Volume in Honour of William Fulton's 80th Birthday', LMS Lecture Note Series (to appear).
Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 10-9 (2016).
Curves disjoint from a nef divisor (with J. Lesieutre). Michigan Mathematical Journal 65 (2016), 321-332.
On subvarieties with ample normal bundle. Journal of the European Mathematical Society 18 (2016), 2459-2468
Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift 280 (2015), 135-148
Partially ample line bundles on toric varieties. (with N. Broomhead and A. Prendergast-Smith). Glasgow Math. J. 58 (2016)
Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant) Mathematical Programming 151 (2), 585-612 (2015).
Ample subvarieties and q -ample divisors. Advances in Mathematics 229 (2012), 2868-2887.
Components of the Hilbert scheme of space curves on low-degree smooth surfaces (with J. O. Kleppe). International Journal of Mathematics Vol. 26, (2015)
Algebraic boundaries of Hilbert's SOS cones (with G. Blekherman, J. Hauenstein, K. Ranestad and B. Sturmfels). Compositio Mathematica 148 (2012).
The Cox ring of a K3 surface of Picard number two. Journal of Pure and Applied Algebra 217 (2013), 709-715.
On the Cox Ring of P2 Blown Up in Points on a Line. Mathematica Scandinavica 9, (2011), 21-31.

Other

Positivity of the diagonal. Oberwolfach Report (2017)
Mori dream hypersurfaces. Oberwolfach Report (2014)
Positivity of higher codimension cycles. Summer school notes, Vlieland, September 2016.
Introduction to Schemes (with G. Ellingsrud) Lecture notes in algebraic geometry.

Ottem, John Christian; Itenberg, Ilia & Degtyarev, Alex (2023). Planes in cubic fourfolds . Algebraic Geometry. ISSN 2313-1691.
Ottem, John Christian & Nicaise, Johannes (2022). Tropical degenerations and stable rationality . Duke mathematical journal. ISSN 0012-7094. doi: https%3A/doi.org/10.1215/00127094-2022-0065.
Nicaise, Johannes & Ottem, John Christian (2021). A refinement of the motivic volume, and specialization of birational types. Progress in Mathematics. ISSN 0743-1643. 342, s. 299–322. doi: 10.1007/978-3-030-75421-1. Fulltekst i vitenarkiv
Benoist, Olivier & Ottem, John Christian (2021). Two coniveau filtrations . Duke mathematical journal. ISSN 0012-7094. 170(12), s. 2719–2753. doi: 10.1215/00127094-2021-0055. Fulltekst i vitenarkiv
Gounelas, Frank & Ottem, John Christian (2020). Remarks on the positivity of the cotangent bundle of a K3 surface. Épijournal de Géométrie Algébrique (EPIGA). ISSN 2491-6765. 4(8). doi: 10.46298/epiga.2020.volume4.5924. Fulltekst i vitenarkiv
Benoist, Olivier & Ottem, John Christian (2020). Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero . Commentarii Mathematici Helvetici. ISSN 0010-2571. 95, s. 27–35. doi: 10.4171/CMH/479. Fulltekst i vitenarkiv
Ottem, John Christian & Suzuki, Fumiaki (2020). A pencil of Enriques surfaces with non-algebraic integral Hodge classes. Mathematische Annalen. ISSN 0025-5831. 377, s. 183–197. doi: 10.1007/s00208-020-01969-8. Fulltekst i vitenarkiv
Ottem, John Christian (2020). Nef cycles on some hyperkähler fourfolds. arXiv.org. ISSN 2331-8422.
Mongardi, Giovanni & Ottem, John Christian (2019). Curve classes on irreducible holomorphic symplectic varieties. Communications in Contemporary Mathematics. ISSN 0219-1997. 22(7). doi: 10.1142/S0219199719500780. Fulltekst i vitenarkiv
Ottem, John Christian & Schreieder, Stefan (2019). On deformations of quintic and septic hypersurfaces. Journal des Mathématiques Pures et Appliquées. ISSN 0021-7824. 135. doi: 10.1016/j.matpur.2019.12.013. Fulltekst i vitenarkiv
Mongardi, Giovanni & Ottem, John Christian (2019). Curve classes on irreducible holomorphic symplectic varieties . arXiv.org. ISSN 2331-8422. doi: 10.1142/S0219199719500780.
Ottem, John Christian & Gounelas, Frank (2018). Remarks on the positivity of the cotangent bundle of a K3 surface . arXiv.org. ISSN 2331-8422.
Ottem, John Christian & Benoist, Olivier (2018). Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero . Commentarii Mathematici Helvetici. ISSN 0010-2571. doi: 10.4171/cmh/479.
Ottem, John Christian & Schreieder, Stefan (2018). On deformations of quintic and septic hypersurfaces . arXiv.org. ISSN 2331-8422. doi: 10.1016/j.matpur.2019.12.013.
Ottem, John Christian & Rennemo, Jørgen Vold (2018). A counterexample to the birational Torelli problem for Calabi-Yau 3-folds. Journal of the London Mathematical Society. ISSN 0024-6107. 97(3), s. 427–440. doi: 10.1112/jlms.12111. Fulltekst i vitenarkiv Vis sammendrag
The Grassmannian Gr(2,5) is embedded in ℙ9 via the Pl\"ucker embedding. The intersection of two general PGL(10)-translates of Gr(2,5) is a Calabi-Yau 3-fold X, and the intersection of the projective duals of the two translates is another Calabi-Yau 3-fold Y, deformation equivalent to X. Applying results of Kuznetsov and Jiang-Leung-Xie shows that X and Y are derived equivalent, which by a result of Addington implies that their third cohomology groups are isomorphic as polarised Hodge structures. We show that X and Y provide counterexamples to a certain "birational" Torelli statement for Calabi-Yau 3-folds, namely, they are deformation equivalent, derived equivalent, and have isomorphic Hodge structures, but they are not birational.
Lehmann, Brian & Ottem, John Christian (2018). Positivity of the diagonal. Advances in Mathematics. ISSN 0001-8708. 335, s. 664–695. doi: 10.1016/j.aim.2018.07.002. Fulltekst i vitenarkiv Vis sammendrag
We study how the geometry of a projective variety X is reflected in the positivity properties of the diagonal ΔX considered as a cycle on X×X. We analyze when the diagonal is big, when it is nef, and when it is rigid. In each case, we give several implications for the geometric properties of X. For example, when the diagonal is big, we prove that the Hodge groups Hk,0(X) vanish for k>0. We also classify varieties of low dimension where the diagonal is nef and big.
Coskun, Izzet; Lesieutre, John & Ottem, John Christian (2016). Effective cones of cycles on blowups of projective space. Algebra & Number Theory. ISSN 1937-0652. 10(9), s. 1983–2014. doi: 10.2140/ant.2016.10.1983. Vis sammendrag
In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for which these cones are finitely generated. Surprisingly, we discover that for (very) general points, the higher codimension cones behave better than the cones of divisors. For example, for the blow-up Xnr of Pn, n>4, at r very general points, the cone of divisors is not finitely generated as soon as r>n+3, whereas the cone of curves is generated by the classes of lines if r<=2n. In fact, if Xnr is a Mori Dream Space then all the effective cones of cycles on Xnr are finitely generated.
Ottem, John Christian (2016). On subvarieties with ample normal bundle. Journal of the European Mathematical Society (Print). ISSN 1435-9855. 18(11), s. 2459–2468. doi: 10.4171/JEMS/644. Fulltekst i vitenarkiv Vis sammendrag
We show that a pseudoeffective R-divisor has numerical dimension 0 if it is numerically trivial on a subvariety with ample normal bundle. This implies that the cycle class of a curve with ample normal bundle is big, which gives an affirmative answer to a conjecture of Peternell. We also give other positivity properties of such subvarieties.
Ottem, John Christian; Prendergast-Smith, Artie & Broomhead, Nathan (2016). Partially ample line bundles on toric varieties. Glasgow Mathematical Journal. ISSN 0017-0895. 58(3), s. 587–598. doi: 10.1017/S001708951500035X. Vis sammendrag
In this note we study properties of partially ample line bundles on simplicial projective toric varieties. We prove that the cone of q-ample line bundles is a union of rational polyhedral cones, and calculate these cones in examples. We prove a restriction theorem for big q-ample line bundles, and deduce that q-ampleness of the anticanonical bundle is not invariant under flips. Finally we prove a Kodaira-type vanishing theorem for q-ample line bundles.
Lesieutre, John & Ottem, John Christian (2016). Curves disjoint from a nef divisor. The Michigan mathematical journal. ISSN 0026-2285. 65(2), s. 321–332. doi: 10.1307/mmj/1465329015. Vis sammendrag
On a projective surface it is well known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing an effective, nef line bundle on a threefold that is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.
Ottem, John Christian (2015). Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift. ISSN 0025-5874. 280(1), s. 135–148. doi: 10.1007/s00209-015-1415-x.
Kleppe, Jan Oddvar & Ottem, John Christian (2015). Components of the Hilbert scheme of space curves on low-degree smooth surfaces . International Journal of Mathematics. ISSN 0129-167X. 26(2). doi: 10.1142/S0129167X15500172. Fulltekst i vitenarkiv Vis sammendrag
We study maximal families W of the Hilbert scheme, H(d,g)_sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of H(d,g)_sc and we determine dim W. If s = 4 and W is an irreducible component of H(d;g)_sc, then the Picard number of S is at most 2 and we explicitly describe, also for s > 4, non-reduced and generically smooth components in the case Pic(S) is generated by the classes of a line and a smooth plane curve of degree s-1. For curves on smooth cubic surfaces the first author finds new classes of non-reduced components of H(d;g)_sc, thus making progress in proving a conjecture for such families.
Ottem, John Christian (2013). Cox rings of K3 surfaces with Picard number 2. Journal of Pure and Applied Algebra. ISSN 0022-4049. 217(4), s. 709–715. doi: 10.1016/j.jpaa.2012.09.016. Fulltekst i vitenarkiv
Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian & Sturmfels, Bernd (2012). Algebraic boundaries of Hilbert's SOS cones. Compositio Mathematica. ISSN 0010-437X. 148(6), s. 1717–1735. doi: 10.1112/S0010437X12000437. Fulltekst i vitenarkiv
Ottem, John Christian (2012). Ample subvarieties and q-ample divisors. Advances in Mathematics. ISSN 0001-8708. 229(5), s. 2868–2887. doi: 10.1016/j.aim.2012.02.001.
Ottem, John Christian (2011). ON THE COX RING OF P-2 BLOWN UP IN POINTS ON A LINE. Mathematica Scandinavica. ISSN 0025-5521. 109(1), s. 22–30. doi: 10.7146/math.scand.a-15175. Fulltekst i vitenarkiv Vis sammendrag
We show that the blow-up of P^2 in n points on a line has finitely generated Cox ring. We give explicit generators for the ring and calculate its defining ideal of relations.

Se alle arbeider i Cristin

Ottem, John Christian (2021). Enriques surface fibrations with even index.
Ottem, John Christian (2021). Tropical degenerations and stable rationality.
Ottem, John Christian & Ottem, John Christian (2021). Enriques surface fibrations with even index.
Ottem, John Christian (2021). Tropical degenerations and stable rationality.
Ottem, John Christian (2021). Tropical degenerations and stable rationality.
Ottem, John Christian (2020). Enriques surface fibrations with non-algebraic integral Hodge classes.
Ottem, John Christian (2020). Tropical degenerations and stable rationality.
Ottem, John Christian (2020). On (2,3)-fourfolds.
Ottem, John Christian (2020). Tropical degenerations and stable rationality.
Ottem, John Christian (2019). Counterexamples to the integral Hodge conjecture.
Ottem, John Christian (2019). Counterexamples to the integral Hodge conjecture.
Ottem, John Christian (2019). Deformations of hypersurfaces.
Ottem, John Christian (2019). A counterexample to the birational Torelli problem.
Ottem, John Christian (2019). A pencil of Enriques surfaces with non-algebraic integral Hodge classes.
Ottem, John Christian (2019). A pencil of Enriques surfaces with non-algebraic integral Hodge classes.
Ottem, John Christian (2018). Failure of the Integral Hodge conjecture for 3-folds.
Ottem, John Christian (2018). Integral hodge conjecture for holomorphic symplectic varieties.
Ottem, John Christian (2018). Integral Hodge conjecture for threefolds.
Ottem, John Christian (2018). The integral Hodge conjecture for threefolds.
Ottem, John Christian (2018). Positivity of the higher codimension cycles.
Ottem, John Christian (2018). Integral Hodge conjecture for threefolds.
Ottem, John Christian (2018). The birational Torelli problem for Calabi-Yau 3-folds.
Ottem, John Christian (2017). A counterexample to the birational Torelli problem for Calabi Yau threefolds.
Ottem, John Christian (2017). A counterexample to the birational Torelli problem for Calabi-Yau threefolds.
Ottem, John Christian (2017). Nef cycles of higher codimension.
Ottem, John Christian (2017). Semiample line bundles in positive characteristic.
Ottem, John Christian (2017). Nef cycles on some hyperkahler fourfolds.
Ottem, John Christian (2017). Nef cycles on some hyperkahler fourfolds.
Ottem, John Christian (2017). Nef cycles on some hyperkahler manifolds.
Ottem, John Christian (2017). Nef cycles on some hyperkahler manifolds.
Ottem, John Christian (2017). Positivity of the diagonal.
Ottem, John Christian (2017). Positivity of the diagonal.
Ottem, John Christian (2017). The Birational Torelli problem for Calabi-Yau 3-folds.
Ottem, John Christian (2017). Positivity of the diagonal.
Ottem, John Christian (2016). Effective cycles of higher codimension.
Ottem, John Christian (2016). Positivity in higher codimension.
Ottem, John Christian (2016). Nef cycles on hyperkahler manifolds.
Ottem, John Christian (2016). Effective cones of cycles on blow-ups of projective space.
Ottem, John Christian (2016). Effective cycles on blow-ups of projective space.
Ottem, John Christian (2016). Moduli of K3s via Global Torelli.
Ottem, John Christian (2016). Effective cones of cycles on blow-ups of projective space.
Ottem, John Christian (2016). Effective and nef cycles in higher codimension.
Ottem, John Christian (2016). Higher codimension cycles.
Ottem, John Christian (2016). K3 surfaces.
Kleppe, Jan Oddvar & Ottem, John Christian (2012). Components of the Hilbert scheme of space curves on low-degree smooth surfaces. arXiv:1204.4819 [math.AG]. Vis sammendrag
We study maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. For every integer s we give conditions on C under which W is a generically smooth component of H(d,g)_{sc} and we determine dim W. If s=4 and W is an irreducible component of H(d,g)_{sc}, then the Picard number of S is at most 2 and we explicitly describe non-reduced and generically smooth components in the case Pic(S) is generated by the classes of a line and a smooth plane cubic curve. For curves on smooth cubic surfaces we find new classes of non-reduced components of H(d,g)_{sc}, thus making progress in proving a conjecture for such families.