Mathematical Research Letters

Volume 27 (2020)

Number 1

On a question of Dolgachev

Pages: 281 – 299



Marco Pacini (I.M., Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil)

Damiano Testa (Mathematics Institute, University of Warwick, Coventry, United Kingdom)


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 $3$.

The first author was partially supported by CNPq, proc. 200377/2015-9 and 301314/2016-0.

Received 5 June 2018

Accepted 5 July 2018

Published 8 April 2020