John Christian Ottem

Personal webpage

CV

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

1. An O-acyclic variety of even index (with F. Suzuki) (2020)

2. A refinement of the motivic volume, and specialization of birational types (with J. Nicaise) (2020)

3. Two coniveau filtrations (with O. Benoist) (2020)

4. Tropical degenerations and stable rationality (Updated version: Oct 2020) (with J. Nicaise) (2019) Video 1 Video 2 Video 3

5. A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) Mathematische Annalen 377 (2020), 183–197. Video

6. On deformations of quintic and septic hypersurfaces (with S. Schreieder) Journal de Mathématiques Pures et Appliquées 135 (2020), 140-158.

7. Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) Épijournal de Géométrie Algébrique 4 (2020).

8. Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi) Communications in Contemporary Mathematics (2020)

9. Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist). Commentarii Mathematici Helvetici 95 (2020) 27-35.

10. 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

11. Positivity of the diagonal (with B. Lehmann). Advances in Mathematics 335 (2018), 664-695.

12. 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).

13. Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre). Algebra & Number Theory 10-9 (2016).

14. Curves disjoint from a nef divisor (with J. Lesieutre). Michigan Mathematical Journal 65 (2016), 321-332.

15. On subvarieties with ample normal bundle. Journal of the European Mathematical Society 18 (2016), 2459-2468

16. Birational geometry of hypersurfaces in products of projective spaces. Mathematische Zeitschrift 280 (2015), 135-148

17. Partially ample line bundles on toric varieties. (with N. Broomhead and A. Prendergast-Smith). Glasgow Math. J. 58 (2016)

18. Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant) Mathematical Programming 151 (2), 585-612 (2015).

19. Ample subvarieties and q-ample divisors. Advances in Mathematics 229 (2012), 2868-2887.

20. Components of the Hilbert scheme of space curves on low-degree smooth surfaces (with J. O. Kleppe). International Journal of Mathematics Vol. 26, (2015)

21. Algebraic boundaries of Hilbert's SOS cones (with G. Blekherman, J. Hauenstein, K. Ranestad and B. Sturmfels). Compositio Mathematica 148 (2012).

22. The Cox ring of a K3 surface of Picard number two. Journal of Pure and Applied Algebra 217 (2013), 709-715.

23. 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.