On the canonical map of some surfaces isogenous to a product

2017/04/04 by Catanese, Fabrizio · 1 citation
#14J10 #14J29 #14M07 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.01100

Abstract

We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces S of general type with p_g=5,6 whose canonical map has image Σ of very high degree, d=48 for p_g=5, d=56 for p_g=6. And a connected component of the moduli space consisting of surfaces S with K²_S = 40, p_g=4, q=0 whose canonical map has always degree ≥ 2, and, for the general surface, of degree 2 onto a canonical surface Y with K²_Y = 12, p_g=4, q=0. The surfaces we consider are SIP 's, i.e. surfaces S isogenous to a product of curves (C₁ × C₂ )/ G; in our examples the group G is elementary abelian, G = (ℤ/m)^k. We also establish some basic results concerning the canonical maps of any surface isogenous to a product, basing on elementary representation theory.

Cited by

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

Related

• New surfaces with canonical map of high degree
• Examples of surfaces with canonical maps of degree 12, 13, 15, 16 and 18
• Examples of surfaces with canonical maps of maximal degree
• Some surfaces with canonical maps of degree 10, 11 and 14
• Canonical surfaces of higher degree