Om prosjektet
Dette er et prosjekt innenfor fagfeltet algebraisk geometri, som har som overliggende mål å klassifisere og studere algebraiske varianter.
Prosjektet omhandler flere sentrale spørsmål knyttet til algebraiske sykler, birasjonal geometri og Hodgeteori. Hovedtemaet i prosjektet er å utforske hvordan geometrien til en algebraisk varietet gjenspeiles i dens undervarianter med visse spesielle egenskaper. Prototypen på slike er såkalte `positive undervarieteter'; varieter med positive snitttall med andre undervarieteter. Et typisk eksempel er et hyperplansnitt H av en projektiv varietet X; her gir Lefschetz' hyperplanteorem relasjoner mellom kohomologigruppene til X og H.
En liten presentasjon av et av forskningsprosjektene: The Rationality Problem
Forskningsartikler
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Planes in cubic fourfolds (with A. Degtyarev and I. Itenberg) (2021)
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An O-acyclic variety of even index (with F. Suzuki and an appendix by O. Wittenberg) (2020)
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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, 335–366 (2021).
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Two coniveau filtrations (with O. Benoist) Duke Mathematical Journal (to appear)
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Tropical degenerations and stable rationality (Updated version: Oct 2020) (with J. Nicaise) (2019)
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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.
- Huybrechts, D.; Rennemo, J. V. Hochschild Cohomology versus the Jacobian Ring and the Torelli Theorem for Cubic Fourfolds. Algebr. Geom. 2019, 6 (1), 76–99.
- Automorphisms of Hilbert schemes of points on surfaces (P. Belmans, G. Oberdieck, J. V. Rennemo)
- A proof of the Donaldson-Thomas crepant resolution conjecture (S. Beentjes, J. Calabrese, J.V. Rennemo)
- Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points A. Krug, J. V. Rennemo
- Singularities of Restriction Varieties in OG(k,n): S. Adalı.
Finansiering
Norges forskningsråd, FRIPRO - Unge Forskertalenter. Prosjektnummer 250104, totalt budsjett ca 9,2 millioner kroner.
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