Derived invariance of the number of holomorphic 1-forms and vector fields

Mihnea Popa; Christian Schnell

doi:10.24033/asens.2149

Derived invariance of the number of holomorphic 1-forms and vector fields

Mihnea Popa^*, Christian Schnell

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.

Original language	English (US)
Pages (from-to)	527-536
Number of pages	10
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	44
Issue number	3
DOIs	https://doi.org/10.24033/asens.2149
State	Published - 2011

ASJC Scopus subject areas

General Mathematics

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abstract = "We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.",

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Derived invariance of the number of holomorphic 1-forms and vector fields

Abstract

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