New surfaces with canonical map of high degree

2018/07/31 by Gleissner, Christian, Pignatelli, Roberto, Rito, Carlos · 1 citation
#14J10 #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.11854

Abstract

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.

Cited by

• Pluricanonical Geometry of Varieties Isogenous to a Product and Abelian Covers

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