Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Autoequivalences of derived category of a K3 surface and monodromy transformations


Authors: Shinobu Hosono, Bong H. Lian, Keiji Oguiso and Shing-Tung Yau
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 513-545
DOI: https://doi.org/10.1090/S1056-3911-04-00364-9
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 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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Additional Information

Shinobu Hosono
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro-ku, Tokyo 153-8914, Japan
Email: hosono@ms.u-tokyo.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 Meguro-ku, Tokyo 153-8914, Japan
Email: oguiso@ms.u-tokyo.ac.jp

Shing-Tung Yau
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Email: yau@math.harvard.edu

DOI: https://doi.org/10.1090/S1056-3911-04-00364-9
Received by editor(s): February 1, 2002
Received by editor(s) in revised form: September 18, 2002
Published electronically: January 15, 2004

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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