Some remarks on the group of derived autoequivalences

Abstract

We prove that the neutral component of the group of derived autoequivalences of a smooth projective variety is the semi-direct product of the neutral component of its Picard group and its group of automorphisms. We use this result to prove several results concerning pairs of derived equivalent varieties.

arXiv comment8 pages

References in corpus (4)

• Semiorthogonal decomposition for algebraic varieties
• Derived categories of coherent sheaves on abelian varieties and equivalences between them
• Some finiteness results for Fourier-Mukai partners
• On derived equivalence classes of algebraic varieties

Cited by in corpus (2)

• Nonexistence of semiorthogonal decompositions and sections of the canonical bundle
• Derived invariants of irregular varieties and Hochschild homology