K3 Surfaces Associated with Curves of Genus Two

  title={K3 Surfaces Associated with Curves of Genus Two},
  author={Abhinav Kumar},
  journal={International Mathematics Research Notices},
  • Abhinav Kumar
  • Published 24 January 2007
  • Mathematics
  • International Mathematics Research Notices
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 ℙ 1 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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Historical Note.- References.- The Content of the Book.- Standard Notations.- I. Preliminaries.- Topology and Algebra.- 1. Notations and Basic Facts.- 2. Some Properties of Bilinear forms.- 3. Vector