Effective Reconstruction of Generic Genus 5 Curves from their Theta Hyperplanes

Abstract

We effectively reconstruct the set of enveloping quadrics of a generic curve C of genus 5 from its theta hyperplanes; for a generic genus 5 curve C this data suffices to effectively reconstruct C. As a consequence we get a complete description of the Schottky locus in genus 5 in terms of theta hyperplanes. The computational part of the proof is a certified numerical argument.

Keywords:

• Reconstruction
• Schottky
• algebraic curve
• theta hyperplane

Mathematics Subject Classification:

• 14H40
• 14Q20

Acknowledgments

I would like to thank T. Celik and A. Kulkarni for many useful remarks they gave on an early draft of this paper.