John Christian Ottem

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
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An O-acyclic variety of even index (with F. Suzuki) (2020)
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A refinement of the motivic volume, and specialization of birational types (with J. Nicaise) (2020)
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Two coniveau filtrations (with O. Benoist) (2020)
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Tropical degenerations and stable rationality (Updated version: Oct 2020) (with J. Nicaise) (2019) Video 1 Video 2 Video 3
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A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) Mathematische Annalen 377 (2020), 183–197. Video
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On deformations of quintic and septic hypersurfaces (with S. Schreieder) Journal de Mathématiques Pures et Appliquées 135 (2020), 140-158.
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Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) Épijournal de Géométrie Algébrique 4 (2020).
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Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) Communications in Contemporary Mathematics (2020)
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Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). Commentarii Mathematici Helvetici 95 (2020) 27-35.
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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
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Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664-695.
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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).
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Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 10-9 (2016).
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Curves disjoint from a nef divisor (with J. Lesieutre). Michigan Mathematical Journal 65 (2016), 321-332.
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On subvarieties with ample normal bundle. Journal of the European Mathematical Society 18 (2016), 2459-2468
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Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift 280 (2015), 135-148
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Partially ample line bundles on toric varieties. (with N. Broomhead and A. Prendergast-Smith). Glasgow Math. J. 58 (2016)
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Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant) Mathematical Programming 151 (2), 585-612 (2015).
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Ample subvarieties and q-ample divisors. Advances in Mathematics 229 (2012), 2868-2887.
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Components of the Hilbert scheme of space curves on low-degree smooth surfaces (with J. O. Kleppe). International Journal of Mathematics Vol. 26, (2015)
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Algebraic boundaries of Hilbert's SOS cones (with G. Blekherman, J. Hauenstein, K. Ranestad and B. Sturmfels). Compositio Mathematica 148 (2012).
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The Cox ring of a K3 surface of Picard number two. Journal of Pure and Applied Algebra 217 (2013), 709-715.
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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.
Publikasjoner
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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
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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
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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
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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
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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
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Ottem, John Christian (2020). Nef cycles on some hyperkähler fourfolds. arXiv.org. ISSN 2331-8422.
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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
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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
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Mongardi, Giovanni & Ottem, John Christian (2019). Curve classes on irreducible holomorphic symplectic varieties . arXiv.org. ISSN 2331-8422. doi: 10.1142/S0219199719500780.
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Ottem, John Christian & Gounelas, Frank (2018). Remarks on the positivity of the cotangent bundle of a K3 surface . arXiv.org. ISSN 2331-8422.
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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.
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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.
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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.
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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
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Ottem, John Christian (2021). Enriques surface fibrations with even index.
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Ottem, John Christian (2021). Tropical degenerations and stable rationality.
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Ottem, John Christian & Ottem, John Christian (2021). Enriques surface fibrations with even index.
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Ottem, John Christian (2021). Tropical degenerations and stable rationality.
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Ottem, John Christian (2021). Tropical degenerations and stable rationality.
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Ottem, John Christian (2020). Enriques surface fibrations with non-algebraic integral Hodge classes.
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Ottem, John Christian (2020). Tropical degenerations and stable rationality.
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Ottem, John Christian (2020). On (2,3)-fourfolds.
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Ottem, John Christian (2020). Tropical degenerations and stable rationality.
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Ottem, John Christian (2019). Counterexamples to the integral Hodge conjecture.
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Ottem, John Christian (2019). Counterexamples to the integral Hodge conjecture.
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Ottem, John Christian (2019). Deformations of hypersurfaces.
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Ottem, John Christian (2019). A counterexample to the birational Torelli problem.
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Ottem, John Christian (2019). A pencil of Enriques surfaces with non-algebraic integral Hodge classes.
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Ottem, John Christian (2019). A pencil of Enriques surfaces with non-algebraic integral Hodge classes.
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Ottem, John Christian (2018). Failure of the Integral Hodge conjecture for 3-folds.
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Ottem, John Christian (2018). Integral hodge conjecture for holomorphic symplectic varieties.
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Ottem, John Christian (2018). Integral Hodge conjecture for threefolds.
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Ottem, John Christian (2018). The integral Hodge conjecture for threefolds.
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Ottem, John Christian (2018). Positivity of the higher codimension cycles.
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Ottem, John Christian (2018). Integral Hodge conjecture for threefolds.
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Ottem, John Christian (2018). The birational Torelli problem for Calabi-Yau 3-folds.
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Ottem, John Christian (2017). A counterexample to the birational Torelli problem for Calabi Yau threefolds.
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Ottem, John Christian (2017). A counterexample to the birational Torelli problem for Calabi-Yau threefolds.
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Ottem, John Christian (2017). Nef cycles of higher codimension.
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Ottem, John Christian (2017). Semiample line bundles in positive characteristic.
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Ottem, John Christian (2017). Nef cycles on some hyperkahler fourfolds.
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Ottem, John Christian (2017). Nef cycles on some hyperkahler fourfolds.
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Ottem, John Christian (2017). Nef cycles on some hyperkahler manifolds.
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Ottem, John Christian (2017). Nef cycles on some hyperkahler manifolds.
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Ottem, John Christian (2017). Positivity of the diagonal.
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Ottem, John Christian (2017). Positivity of the diagonal.
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Ottem, John Christian (2017). The Birational Torelli problem for Calabi-Yau 3-folds.
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Ottem, John Christian (2017). Positivity of the diagonal.
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Ottem, John Christian (2016). Effective cycles of higher codimension.
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Ottem, John Christian (2016). Positivity in higher codimension.
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Ottem, John Christian (2016). Nef cycles on hyperkahler manifolds.
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Ottem, John Christian (2016). Effective cones of cycles on blow-ups of projective space.
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Ottem, John Christian (2016). Effective cycles on blow-ups of projective space.
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Ottem, John Christian (2016). Moduli of K3s via Global Torelli.
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Ottem, John Christian (2016). Effective cones of cycles on blow-ups of projective space.
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Ottem, John Christian (2016). Effective and nef cycles in higher codimension.
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Ottem, John Christian (2016). Higher codimension cycles.
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Ottem, John Christian (2016). K3 surfaces.
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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