## Data:

05/03/2024 - 15:00

## Aula:

Aula Lagrange

## Speaker:

Federico Fallucca

## Categoria:

Seminari di Algebra e Geometria Algebrica

## Afferenza:

Università di Trento

## Descrizione:

**Abstract:**

**A**

**Product-Quotient surface is the minimal resolution of singularities of a quotient of a product of curves by the action of a finite group of automorphisms. Introduced by Catanese in a paper from 2000, Product-Quotient surfaces have been extensively investigated by several authors. They are valuable tools for constructing new examples of algebraic surfaces and exploring their geometry in an accessible way. Consequently, classifying these surfaces by fixing certain invariants such as K^2 and χ is not only inherently interesting but also highly practical in various contexts.**

During the talk, I will provide a brief overview on Product-Quotient surfaces and I will describe the most important tools that are developed by some authors to produce a classification of them using computational algebra systems (e.g. MAGMA).

I will introduce the results I have obtained to provide a more performant algorithm. The main result is a theorem that allows us to move from a database of G-coverings of the projective line (in pairs), already produced in a recent work by Conti, Ghigi and Pignatelli, to a database of families of Product-Quotient surfaces.

Using this approach, I have produced a huge list of families of Product-Quotient surfaces with pg=3, q=0, and high K^2 values. The classification is complete for K^2 equal to 32. Finally, if time permits, I plan to show, as an application, how I used this list to obtain new results on a still open question regarding the degree of the canonical map of surfaces of general type.