Derived invariance of the number of holomorphic 1-forms and vector fields
Algebraic Geometry
2010-10-26 v5
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.
Keywords
Cite
@article{arxiv.0912.4040,
title = {Derived invariance of the number of holomorphic 1-forms and vector fields},
author = {Mihnea Popa and Christian Schnell},
journal= {arXiv preprint arXiv:0912.4040},
year = {2010}
}
Comments
8 pages; final version with small expository changes, to appear in Ann. Sci. ENS; fixed an inaccurate reference