On a question of Dolgachev

Abstract

For each even, positive integer $n$, we define a rational self-map on the space of plane curves of degree $n$, using classical contravariants. In the case of plane quartics, we show that the degree of this map is 15. This answers a question of Dolgachev on the moduli space of curves of genus 3.

15 pages, no figure, to appear in Mathematical Research Letters