Derived autoequivalences and a weighted Beilinson resolution

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Canonaco, Alberto¹  Karp, Robert L.² 

[1] Univ Pavia, Dipartimento Matemat F Casorati, Via Ferrata 1, I-27100 Pavia, Italy

[2] Rutgers State Univ, NHETC, Piscataway, NJ 08854 USA

关键词: derived categories;    Calabi-Yau varieties;    algebraic stacks;   

DOI  :  10.1016/j.geomphys.2008.01.004

来源: Elsevier

【 摘 要 】

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(l). 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. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free