2006/10/27 by Alberto Canonaco, Canonaco, Alberto, Robert L. Karp +1
Mathematics · #14A20 #14J32 #18E30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0610848
openalex publication_date 2006/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Db(X): the first one is induced by the spherical object OX, while the second one is tensoring with OX(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.