$\mathbb P$-objects and autoequivalences of derived categories

D. Huybrechts, R. P. Thomas

Published 2005-07-04, updated 2006-02-05Version 2

We describe new autoequivalences of derived categories of coherent sheaves arising from what we call $\mathbb P^n$-objects of the category. Standard examples arise from holomorphic symplectic manifolds. Under mirror symmetry these autoequivalences should be mirror to Seidel's Dehn twists about lagrangian $\mathbb P^n$ submanifolds. We give various connections to spherical objects and spherical twists, and include a simple description of Atiyah and Kodaira-Spencer classes in an appendix.