2002/01/07 by Shinobu Hosono, Hosono, Shinobu, Bong H. Lian +6
Mathematics · Physics and Astronomy · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG #msc:14J28
paper · pdf · doi:10.48550/arxiv.math/0201047
AMSTeX, 27 pages, 2 figures; reference added, and minor corrections made
openalex publication_date 2002/01/07 · arxiv created 2002/02/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by homological mirror symmetry we also consider the mirror counterpart, i.e. symplectic version of it. In the case of ρ(X)=1, we find an explicit formula which reproduces the number of Fourier-Mukai (FM) partners from the monodromy problem of the mirror K3 family. We present an explicit example in which a monodromy action does not come from an autoequivalence of the mirror side.