Algebraic integrability of foliations with numerically trivial canonical bundle
| Autor: | Thomas Peternell, Andreas Höring |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Mathematisches Institut [Bayreuth], Universität Bayreuth, ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015) |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Class (set theory) General Mathematics Minimal models 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Algebraic number Complex Variables (math.CV) 14J32 37F75 14E30 Algebraic Geometry (math.AG) Projective variety ComputingMilieux_MISCELLANEOUS Flatness (mathematics) Mathematics Chern class Mathematics - Complex Variables 010102 general mathematics [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] 16. Peace & justice Canonical bundle Reflexive sheaf 010307 mathematical physics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| Zdroj: | Inventiones Mathematicae Inventiones Mathematicae, Springer Verlag, 2019, 216 (2), pp.395-419. ⟨10.1007/s00222-018-00853-2⟩ |
| ISSN: | 0020-9910 1432-1297 |
| DOI: | 10.48550/arxiv.1710.06183 |
| Popis: | Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second Chern class does not vanish. Combined with the recent work of Druel and Greb-Guenancia-Kebekus this establishes the Beauville-Bogomolov decomposition for minimal models with trivial canonical class. Comment: 20 pages, removed an assumption from Thm.1.5 |
| Databáze: | OpenAIRE |
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