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

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

2010-05-17

arxiv.org/abs/1005.2866v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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