The group of autoequivalences and the Fourier-Mukai number of a projective manifold

2010/05/17 by Kotaro Kawatani, Kawatani, Kotaro
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1005.2866

7 pages, v2:Question 3.4 were removed and Proposition 3.4 and Corollary 3.5 were added

arxiv created 2010/05/21 · arxiv updated 2010/05/24

Abstract

Let X be a smooth projective variety and \Aut (D(X)) the group of autoequivalences of the derived category of X. In this paper we show that X has no Fourier-Mukai partner other than X when \Aut (D(X)) is generated by shifts, automorphisms and tensor products of line bundles.

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