On the classification of product-quotient surfaces with , and their canonical map

  • Federico Fallucca

    Università degli Studi di Milano-Bicocca, Italy
On the classification of product-quotient surfaces with $q=0$, $p_{g}=3$ and their canonical map cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

In this work, we present new results to produce an algorithm that returns, for any fixed pair of positive integers and , all regular surfaces of general type with self-intersection of the canonical class and Euler characteristic , which are product-quotient surfaces. The key result we obtain is an algebraic characterization of all families of regular product-quotients surfaces, up to isomorphism, arising from a pair of -coverings of . As a consequence of our work, we provide a classification of all regular product-quotient surfaces of general type with and . Furthermore, we study their canonical map and present several new examples of surfaces of general type with a high degree of the canonical map.

Cite this article

Federico Fallucca, On the classification of product-quotient surfaces with , and their canonical map. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 35 (2024), no. 4, pp. 529–596

DOI 10.4171/RLM/1051