Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations

Details Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations Autoequivalences of Derived Category of A K3 Surface and Monodromy Transformations

2002-01-07

arxiv.org/abs/math/0201047v3

Mathematics

Algebraic Geometry

AMSTeX, 27 pages, 2 figures; reference added, and minor corrections made

Scientific paper

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 $\rho(X)=1$, 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.

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