John Christian Ottem
Professor

Algebra, Geometry and Topology
Norwegian version of this page
Email
johnco@math.uio.no
Phone
+47 22855930
Room
1109
Username
Visiting address
Moltke Moes vei 35
Niels Henrik Abels hus
0851 Oslo
Postal address
Postboks 1053 Blindern
0316 Oslo
Research interests
Higher dimensional algebraic geometry, positivity of line bundles and subschemes, CalabiYau manifolds, and the moduli space of curves.
Projects
'Young Research Talents'. Research Council of Norway 20162021.
Teaching
This term I am teaching MAT1110  Calculus and linear algebra and MAT4215  Algebraic Geometry II.
Students
Bernt Ivar Utstøl Nødland (20162019)
Bjørn Skauli (2018)
Martin Helsø (2017, coadvisor)
Elisa Cazzador (2018, coadvisor)
Simen Westbye Moe (2019)
Publications
 Two coniveau filtrations (with O. Benoist) (2020)
 Tropical degenerations and stable rationality (with J. Nicaise) (2019)
 A pencil of Enriques surfaces with nonalgebraic integral Hodge classes (with F. Suzuki) Mathematische Annalen (to appear).
 On deformations of quintic and septic hypersurfaces (with S. Schreieder) Journal de Mathématiques Pures et Appliquées 135 (2020), 140158.
 Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) (2018)
 Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) Communications in Contemporary Mathematics (to appear)
 Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). Commentarii Mathematici Helvetici (to appear)
 A counterexample to the birational Torelli problem for CalabiYau 3folds (with J. V. Rennemo). Journal of the London Mathematical Society 97 (2018), 427440
 Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664695.
 Effective cones of cycles on blowups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 109 (2016).
 Nef cycles on some hyperkahler fourfolds. LMS volume for Fulton 80 (to appear)
 Curves disjoint from a nef divisor (with J. Lesieutre). Michigan Mathematical Journal 65 (2016), 321332.
 On subvarieties with ample normal bundle. Journal of the European Mathematical Society 18 (2016), 24592468
 Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift 280 (2015), 135148
 Partially ample line bundles on toric varieties. (with N. Broomhead and A. PrendergastSmith). Glasgow Math. J. 58 (2016)
 Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant) Mathematical Programming 151 (2), 585612 (2015).
 Ample subvarieties and qample divisors. Advances in Mathematics 229 (2012), 28682887.
 Components of the Hilbert scheme of space curves on lowdegree 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), 709715.
 On the Cox Ring of P2 Blown Up in Points on a Line. Mathematica Scandinavica 9, (2011), 2131.
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.
Publications

Nicaise, Johannes & Ottem, John Christian (2021). A refinement of the motivic volume, and specialization of birational types. Progress in Mathematics. ISSN 07431643. 342. doi: 10.1007/9783030754211. Full text in Research Archive

Ottem, John Christian & Benoist, Olivier (2021). Two coniveau filtrations . Duke mathematical journal. ISSN 00127094. 170(12), p. 2719–2753. doi: 10.1215/0012709420210055. Full text in Research Archive

Gounelas, Frank & Ottem, John Christian (2020). Remarks on the positivity of the cotangent bundle of a K3 surface. Épijournal de Géométrie Algébrique (EPIGA). ISSN 24916765. 4(8). doi: 10.46298/epiga.2020.volume4.5924. Full text in Research Archive

Benoist, Olivier & Ottem, John Christian (2020). Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero . Commentarii Mathematici Helvetici. ISSN 00102571. 95, p. 27–35. doi: 10.4171/CMH/479. Full text in Research Archive

Ottem, John Christian & Suzuki, Fumiaki (2020). A pencil of Enriques surfaces with nonalgebraic integral Hodge classes. Mathematische Annalen. ISSN 00255831. 377, p. 183–197. doi: 10.1007/s00208020019698. Full text in Research Archive

Ottem, John Christian (2020). Nef cycles on some hyperkähler fourfolds. arXiv.org. ISSN 23318422.

Mongardi, Giovanni & Ottem, John Christian (2019). Curve classes on irreducible holomorphic symplectic varieties. Communications in Contemporary Mathematics. ISSN 02191997. 22(7). doi: 10.1142/S0219199719500780. Full text in Research Archive

Ottem, John Christian & Schreieder, Stefan (2019). On deformations of quintic and septic hypersurfaces. Journal des Mathématiques Pures et Appliquées. ISSN 00217824. 135. doi: 10.1016/j.matpur.2019.12.013. Full text in Research Archive

Mongardi, Giovanni & Ottem, John Christian (2019). Curve classes on irreducible holomorphic symplectic varieties . arXiv.org. ISSN 23318422. 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 23318422.

Ottem, John Christian & Benoist, Olivier (2018). Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero . Commentarii Mathematici Helvetici. ISSN 00102571. doi: 10.4171/cmh/479.

Ottem, John Christian & Schreieder, Stefan (2018). On deformations of quintic and septic hypersurfaces . arXiv.org. ISSN 23318422. doi: 10.1016/j.matpur.2019.12.013.

Ottem, John Christian & Rennemo, Jørgen Vold (2018). A counterexample to the birational Torelli problem for CalabiYau 3folds. Journal of the London Mathematical Society. ISSN 00246107. 97(3), p. 427–440. doi: 10.1112/jlms.12111. Full text in Research Archive Show summary

Lehmann, Brian & Ottem, John Christian (2018). Positivity of the diagonal. Advances in Mathematics. ISSN 00018708. 335, p. 664–695. doi: 10.1016/j.aim.2018.07.002. Full text in Research Archive Show summary

Coskun, Izzet; Lesieutre, John & Ottem, John Christian (2016). Effective cones of cycles on blowups of projective space. Algebra & Number Theory. ISSN 19370652. 10(9), p. 1983–2014. doi: 10.2140/ant.2016.10.1983. Show summary

Ottem, John Christian (2016). On subvarieties with ample normal bundle. Journal of the European Mathematical Society (Print). ISSN 14359855. 18(11), p. 2459–2468. doi: 10.4171/JEMS/644. Full text in Research Archive Show summary

Ottem, John Christian; PrendergastSmith, Artie & Broomhead, Nathan (2016). Partially ample line bundles on toric varieties. Glasgow Mathematical Journal. ISSN 00170895. 58(3), p. 587–598. doi: 10.1017/S001708951500035X. Show summary

Lesieutre, John & Ottem, John Christian (2016). Curves disjoint from a nef divisor. The Michigan mathematical journal. ISSN 00262285. 65(2), p. 321–332. doi: 10.1307/mmj/1465329015. Show summary

Ottem, John Christian (2015). Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift. ISSN 00255874. 280(1), p. 135–148. doi: 10.1007/s002090151415x.

Kleppe, Jan Oddvar & Ottem, John Christian (2015). Components of the Hilbert scheme of space curves on lowdegree smooth surfaces . International Journal of Mathematics. ISSN 0129167X. 26(2). doi: 10.1142/S0129167X15500172. Full text in Research Archive Show summary

Ottem, John Christian (2013). Cox rings of K3 surfaces with Picard number 2. Journal of Pure and Applied Algebra. ISSN 00224049. 217(4), p. 709–715. doi: 10.1016/j.jpaa.2012.09.016. Full text in Research Archive

Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian & Sturmfels, Bernd (2012). Algebraic boundaries of Hilbert's SOS cones. Compositio Mathematica. ISSN 0010437X. 148(6), p. 1717–1735. doi: 10.1112/S0010437X12000437. Full text in Research Archive

Ottem, John Christian (2012). Ample subvarieties and qample divisors. Advances in Mathematics. ISSN 00018708. 229(5), p. 2868–2887. doi: 10.1016/j.aim.2012.02.001.

Ottem, John Christian (2011). ON THE COX RING OF P2 BLOWN UP IN POINTS ON A LINE. Mathematica Scandinavica. ISSN 00255521. 109(1), p. 22–30. doi: 10.7146/math.scand.a15175. Full text in Research Archive Show summary

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 nonalgebraic 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 nonalgebraic integral Hodge classes.

Ottem, John Christian (2019). A pencil of Enriques surfaces with nonalgebraic integral Hodge classes.

Ottem, John Christian (2018). Failure of the Integral Hodge conjecture for 3folds.

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 CalabiYau 3folds.

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 CalabiYau 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 CalabiYau 3folds.

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 blowups of projective space.

Ottem, John Christian (2016). Effective cycles on blowups of projective space.

Ottem, John Christian (2016). Moduli of K3s via Global Torelli.

Ottem, John Christian (2016). Effective cones of cycles on blowups 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 lowdegree smooth surfaces. arXiv:1204.4819 [math.AG]. Show summary
Published Jan. 6, 2016 9:05 AM
 Last modified Apr. 9, 2021 8:22 AM