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Derived autoequivalences and a weighted Beilinson resolution

Alberto Canonaco·Robert L. Karp
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Abstract

Given a smooth stacky Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D^b(X): the first one is induced by the spherical object O_X, while the second one is tensoring with O_X(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights of the weighted projective space, is isomorphic to the autoequivalence "shift by 2". The proof also involves the construction of a Beilinson type resolution of the diagonal for weighted projective spaces, viewed as smooth stacks.

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Alberto Canonaco, Robert L. Karp. 2007-12-30. Derived autoequivalences and a weighted Beilinson resolution. https://arxiv.org/abs/math/0610848

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