Monodromy and birational geometry of O'Grady's sixfolds
| Autor: | Antonio Rapagnetta, Giovanni Mongardi |
|---|---|
| Přispěvatelé: | Mongardi, Giovanni, Rapagnetta, Antonio |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General Mathematics Lagrangian fibration Lattice (discrete subgroup) 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry O’Grady’s sixfoldsMonodromy groupAmple coneLagrangian fibration 0103 physical sciences FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Zero divisor Hyperkähler manifold Mathematics Group (mathematics) Applied Mathematics 010102 general mathematics Fibration Birational geometry Settore MAT/03 Monodromy group O'Grady's sixfolds Monodromy 010307 mathematical physics Mathematics::Differential Geometry Ample cone Hodge structure |
| Popis: | We prove that the bimeromorphic class of a hyperk\"ahler manifold deformation equivalent to O'Grady's six dimensional one is determined by the Hodge structure of its Beauville-Bogomolov lattice by showing that the monodromy group is maximal. As applications, we give the structure for the K\"ahler and the birational K\"ahler cones in this deformation class and we prove that the existence of a square zero divisor implies the existence a rational lagrangian fibration with fixed fibre types. Comment: Final version, to appear in JMPA |
| Databáze: | OpenAIRE |
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