[Dottorcomp] Seminario di Geometria - MatApp [Geometry seminar - MatApp] in Bicocca

[Lidia Stoppino]

Carissimi, giro un messaggio da Sonia Brivio su due seminari in Bicocca il 13 maggio:

[English version below]
Carissimi,

lunedì 13 maggio, dalle ore 14:00 in aula 2109 (edificio U5) i due nuovi assegnisti del gruppo di Geometria del nostro Dipartimento terranno i seguenti seminari (gli abstract in calce al messaggio):

On the classification of regular product-quotient surfaces with p_g=3 and their canonical map 
Federico Fallucca

Special structures and spinors on manifolds
Romeo Segnan Dalmasso

Vi preghiamo di diffondere questo messaggio a chi potesse essere interessato.

Un saluto,
Sonia Brivio
Samuele Mongodi

-----------------------------------------------------------------------------------

Dear all,

on Monday, May 13th, from 2:00 PM in room 2109 (U5 building), the two new post-docs of the Geometry group of our Department will give the following talks (abstracts below):

On the classification of regular product-quotient surfaces with p_g=3 and their canonical map 
Federico Fallucca

Special structures and spinors on manifolds
Romeo Segnan Dalmasso

Please, forward this message to anyone who may be interested.

Best regards,
Sonia Brivio
Samuele Mongodi

--------------------------------------------------------------------------------------

On the classification of regular product-quotient surfaces with p_g=3 and their canonical map 
Federico Fallucca

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 the self-intersection $K^2$ of the canonical class and the Euler characteristic $\chi$ 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 a computational algebra system (e.g. MAGMA).
I will introduce the results I have obtained to provide a more efficient algorithm. One of the main results 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 $p_g=3$, $q=0$, and high $K^2$ values. The classification is complete for $K^2\in \{23, ..., 32\}$. 
Finally, I plan to show as an application how I used this huge list of families to obtain new results on a still open question regarding the degree of the canonical map of surfaces of general type.

--------------------------------------------------------------------------------------

Special structures and spinors on manifolds
Romeo Segnan Dalmasso

Abstract: The study of special structures on (pseudo)-Riemannian manifolds has been of interest for both mathematicians and physicists for at least a century, the most striking example being the Einstein condition on the metric tensor of the manifold, which is hence called Einstein.

The existence of such structures on a given manifold, is closely related to (the existence of) sections of the spinor bundle, called spinors, satisfying some constraint. For instance, the existence of Killing spinors on a Riemannian (spin) manifold implies, among other things, that the metric satisfies the Einstein condition, and the existence of parallel spinors implies that the Ricci tensor is identically zero. In the pseudo-Riemannian setting the situation is less studied, nor as strict, for instance the metric need not be Einstein.

In this talk, I will first give an introduction to the topic, which aims to give a more clear picture of the relation between special structures and particular spinors. Next, I will present a new method to construct pseudo-Riemannian K\"ahler Einstein and Sasaki Einstein solvmanifolds, which come equipped with a parallel or Killing spinors respectively. Finally, I will talk about possible future work on the construction of manifolds endowed with parallel or Killing spinors.

This talk is based on joint works with D. Conti and F.A. Rossi.



Lidia Stoppino
Dipartimento di Matematica
Università di Pavia
Via Ferrata 5
27100 Pavia
Ufficio C.07 (primo piano)
Tel. +39 0382 985624
e-mail: lidia.stoppino a unipv.it 
pagina web: http://www.stoppino.it