Proof of a Conjecture of Batyrev and Nill

Abstract

We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an associated category of singularities and toric variation of geometric invariant theory quotients.

arXiv comment23 pages. To appear in American Journal of Mathematics. Minor corrections