Communications in Analysis and Geometry
Volume 30 (2022)
New surfaces with canonical map of high degree
Pages: 1811 – 1823
We give an algorithm that, for a given value of the geometric genus $p_g$, computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and have canonical system with at most isolated base points. We use it to show that there are exactly two families of such surfaces with canonical map of degree $32$. We also construct a surface with $q = 1$ and canonical map of degree $24$. These are regular surfaces with $p_g = 3$ and base point free canonical system. We discuss the case of regular surfaces with $p_g = 4$ and base point free canonical system.
Received 11 October 2018
Accepted 17 March 2020
Published 13 July 2023