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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm165, 26 pages, doi:10.1093/imrn/rnm165 published on February 11, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

K3 Surfaces Associated with Curves of Genus Two

Abhinav Kumar

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

Correspondence: Correspondence to be sent to: abhinav{at}math.mit.edu

It is known ([10, 27]) that there is a unique K3 surface X which corresponds to a genus 2 curve C such that X has a Shioda–Inose structure with quotient birational to the Kummer surface of the Jacobian of C. In this paper we give an explicit realization of X as an elliptic surface over P1 with specified singular fibers of type II* and III*. We describe how the Weierstrass coefficients are related to the Igusa–Clebsch invariants of C.


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