Curves of genus 2 and Desargues configurations

Abstract

We study the moduli space M_D of Desargues configurations and how to define a holomorphic map from M_D to M^b_6 the moduli space of stable binary forms of degree 6. The construction of the map goes back to the greek mathematician C. Stephanos who published a paper about this in 1883, using classical geometric invariant theory. We put this in a contemporary context and give a new proof of the properties of the map.We also study degenerations.