John Christian Ottem

Department of Mathematics
University of Oslo
Box 1053, Blindern
0316 Oslo, Norway

Office: B1109


My research interests are in algebraic geometry, in particular birational geometry, Calabi-Yau manifolds, and Hodge theory.

Algebraic geometry group at UiO
Algebra/algebraic geometry seminar at UiO.



Moduli and Algebraic Cycles Research programme at the Mittag-Leffler Institute, Fall 2021.
Enumeration and Moduli: A conference in algebraic geometry on the occasion of Geir Ellingsrud's 70th birthday. December 6-8 2018, University of Oslo.
Combinatorics and Hodge theory. 18-22 June 2018, Sophus Lie Conference Center, Nordfjordeid, Norway.
Geometry of Moduli. August 7, 2017 - Aug. 11, 2017, Lofoten, Norway.
Polar geometry: A conference celebrating the work of Ragni Piene on the occasion of her 70th birthday. January 26-28, 2017, University of Oslo.
Nordfjordeid Summer School: Stability conditions on triangulated categories and geometric applications. June 13-17, 2016, Sophus Lie Conference Center, Nordfjordeid, Norway.


  1. Tropical degenerations and stable rationality (with J. Nicaise) (2019)
  2. A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) (2019)
  3. On deformations of quintic and septic hypersurfaces (with S. Schreieder) (2018)
    Journal de Mathématiques Pures et Appliquées (to appear)
  4. Remarks on the positivity of the cotangent bundle of a K3 surface (with F. Gounelas) (2018)
  5. Curve classes on irreducible holomorphic symplectic varieties (with G. Mongardi)
    Communications in Contemporary Mathematics (to appear)
  6. Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero (with O. Benoist).
    Commentarii Mathematici Helvetici (to appear)
  7. 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
  8. Positivity of the diagonal (with B. Lehmann).
    Advances in Mathematics 335 (2018), 664-695.
  9. Effective cones of cycles on blow-ups of projective space (with I. Coskun, J. Lesieutre).
    Algebra & Number Theory 10-9 (2016).
  10. Nef cycles on some hyperkahler fourfolds.
    LMS volume for Fulton 80 (to appear)
  11. Curves disjoint from a nef divisor (with J. Lesieutre).
    Michigan Mathematical Journal 65 (2016), 321-332.
  12. On subvarieties with ample normal bundle.
    Journal of the European Mathematical Society 18 (2016), 2459-2468
  13. Birational geometry of hypersurfaces in products of projective spaces.
    Mathematische Zeitschrift 280 (2015), 135-148
  14. Quartic spectrahedra (with K. Ranestad, B. Sturmfels, C. Vinzant)
    Math. Prog. B (2015).
  15. Ample subvarieties and q-ample divisors.
    Advances in Mathematics 229 (2012), 2868-2887.
  16. Partially ample line bundles on toric varieties. (with N. Broomhead and A. Prendergast-Smith).
    Glasgow Math. J. 58 (2016)
  17. Algebraic boundaries of Hilbert's SOS cones (with G. Blekherman, J. Hauenstein, K. Ranestad and B. Sturmfels).
    Compositio Mathematica 148 (2012).
  18. Components of the Hilbert scheme of space curves on low-degree smooth surfaces (with J. O. Kleppe).
    International Journal of Mathematics Vol. 26, (2015)
  19. The Cox ring of a K3 surface of Picard number two.
    Journal of Pure and Applied Algebra 217 (2013), 709-715.
  20. On the Cox Ring of P2 Blown Up in Points on a Line.
    Mathematica Scandinavica 9, (2011), 21-31.



Bernt Ivar Utstøl Nødland (2016-2019)
Bjørn Skauli (2018-)
Simen Westbye Moe


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