English

Derived autoequivalences and a weighted Beilinson resolution

Algebraic Geometry 2007-12-30 v2

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.

Cite

@article{arxiv.math/0610848,
  title  = {Derived autoequivalences and a weighted Beilinson resolution},
  author = {Alberto Canonaco and Robert L. Karp},
  journal= {arXiv preprint arXiv:math/0610848},
  year   = {2007}
}

Comments

19 pages; minor modifications; accepted by J. Geom. Phys

R2 v1 2026-07-22T17:45:09.029Z