Correspondences between K3 surfaces

Details Correspondences between K3 surfaces Correspondences between K3 surfaces

2002-11-07

arxiv.org/abs/math/0211129v2

Mathematics

Algebraic Geometry

With an appendix by Igor Dolgachev. To appear on the Michigan Mathematical Journal. 19 pages, LaTex with xy-pic,1 figure

Scientific paper

In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show the existence of a correspondence between a general $K3$ surface with $\rho =17$ and a Kummer surface having transcendental lattices $\QQ$-Hodge isomorphic.

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