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

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

2005-07-04

arxiv.org/abs/math/0507040v2

Mathematical Research Letters 13, 87--98, 2006

Mathematics

Algebraic Geometry

13 pages. Published version, minor corrections

Scientific paper

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.

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