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

2009/12/20 by Popa, Mihnea, Schnell, Christian · 1 citation
#14F05 #14K30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.4040

Abstract

We prove that smooth projective varieties with equivalent derived categories have isogenous (and sometimes isomorphic) Picard varieties. In particular their irregularity and number of independent vector fields are the same. This is turn implies, in combination with the invariance of Hochschild homology, that all Hodge numbers are the same for arbitrary derived equivalent threefolds.

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