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

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

2009-12-20

arxiv.org/abs/0912.4040v5

Mathematics

Algebraic Geometry

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

Scientific paper

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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