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

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.

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