A note on mapping class group actions on derived categories

Sibilla, Nicolò

doi:10.1090/S0002-9939-2014-11914-9

A note on mapping class group actions on derived categories
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by Nicolò Sibilla PDF

Proc. Amer. Math. Soc. 142 (2014), 1837-1848 Request permission

Abstract:

Let $X_n$ be a cycle of $n$ projective lines and $\mathbb {T}_n$ a symplectic torus with $n$ punctures. Using the theory of spherical twists introduced by Seidel and Thomas, the author will define an action of the pure mapping class group of $\mathbb {T}_n$ on $D^b(Coh(X_n))$. The motivation comes from homological mirror symmetry for degenerate elliptic curves, which was studied by the author with Treumann and Zaslow.

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