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

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.

arXiv comment8 pages; final version with small expository changes, to appear in Ann. Sci. ENS; fixed an inaccurate reference

References in corpus (2)

• The Mukai pairing, I: the Hochschild structure
• Remarks on derived equivalences of Ricci-flat manifolds

Cited by in corpus (1)

• The Brauer group is not a derived invariant