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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Planes in cubic fourfolds (with A. Degtyarev and I. Itenberg) Algebraic Geometry (to appear)
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An O-acyclic variety of even index (with F. Suzuki, and an appendix by O. Wittenberg) Mathematische Annalen (to appear)
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Tropical degenerations and stable rationality (with J. Nicaise) Duke Mathematical Journal 171 (2022), 3023 - 3075,
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A refinement of the motivic volume, and specialization of birational types (with J. Nicaise) Rationality of Varieties, Progress in Mathematics 342, 291-322 (2021).
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Two coniveau filtrations (with O. Benoist) Duke Mathematical Journal 170 (2021) 2719-2753
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A pencil of Enriques surfaces with non-algebraic integral Hodge classes (with F. Suzuki) Mathematische Annalen 377 (2020), 183–197.
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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' (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.