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

D. Huybrechts·R. P. Thomas
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Abstract

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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D. Huybrechts, R. P. Thomas. 2006-02-05. $\mathbb P$-objects and autoequivalences of derived categories. https://arxiv.org/abs/math/0507040

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