Autoequivalences of derived category of a K3 surface and monodromy transformations
Authors:
Shinobu Hosono, Bong H. Lian, Keiji Oguiso and ShingTung Yau
Journal:
J. Algebraic Geom. 13 (2004), 513545
DOI:
https://doi.org/10.1090/S1056391104003649
Published electronically:
January 15, 2004
MathSciNet review:
2047679
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Abstract  References  Additional Information
Abstract: 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., the symplectic version of it. In the case of $\rho (X)=1$, we find an explicit formula which reproduces the number of FourierMukai (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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Additional Information
Shinobu Hosono
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguroku, Tokyo 1538914, Japan
Email:
hosono@ms.utokyo.ac.jp
Bong H. Lian
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02154
Email:
lian@brandeis.edu
Keiji Oguiso
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguroku, Tokyo 1538914, Japan
Email:
oguiso@ms.utokyo.ac.jp
ShingTung Yau
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
MR Author ID:
185480
ORCID:
0000000333942187
Email:
yau@math.harvard.edu
Received by editor(s):
February 1, 2002
Received by editor(s) in revised form:
September 18, 2002
Published electronically:
January 15, 2004