Page 107 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 107
ARITHMETIC AND GEOMETRY OF ALGEBRAIC SURFACES (MS-45)
Z/2-Godeaux surfaces
Carlos Rito, crito@fc.up.pt
University of Porto - CMUP, Portugal
I will report on work in progress in collaboration with Eduardo Dias towards the classification
of Z/2-Godeaux surfaces.
Generalized Kummer surfaces and a configuration of conics in the plane
Alessandra Sarti, alessandra.sarti@univ-poitiers.fr
University of Poitiers, France
A generalized Kummer surface is the minimal resolution of the quotient of an abelian surface by
an automorphism of order three. The quotient surface contains nine cusps and this is a special
example of a singular K3 surface. The converse is also true : the minimal resolution of a K3
surface containing nine cusps is a generalized Kummer surface. In this paper we study several
configurations of nine cusps on the same K3 surface, which is the double cover of the plane
ramified on a sextic with nine cusps. We get the new configurations by studying conics through
the singular points of the sextic. The aim of the construction is to investigate the following
question: is it possible that the K3 surface is the generalized Kummer surface associated to two
non-isomorphic abelian surfaces ? This is a joint work with D. Kohl and X. Roulleau.
Holomorphic one forms on projective surfaces and applications
Sara Torelli, sara.torelli7@gmail.com
University of Hannover, Germany
In the talk I present a result, recently proven in collaboration with F.Favale and G.P.Pirola, that
aims to recover holomorphic 1-forms on smooth projective surfaces from divisors contracted
to points by big and semiample line bundles. I’ll then discuss its application to investigate
holomorphic forms on higher dimensional varieties (e.g. the moduli space of pointed curves
Mg,n) and related open problems.
105
Z/2-Godeaux surfaces
Carlos Rito, crito@fc.up.pt
University of Porto - CMUP, Portugal
I will report on work in progress in collaboration with Eduardo Dias towards the classification
of Z/2-Godeaux surfaces.
Generalized Kummer surfaces and a configuration of conics in the plane
Alessandra Sarti, alessandra.sarti@univ-poitiers.fr
University of Poitiers, France
A generalized Kummer surface is the minimal resolution of the quotient of an abelian surface by
an automorphism of order three. The quotient surface contains nine cusps and this is a special
example of a singular K3 surface. The converse is also true : the minimal resolution of a K3
surface containing nine cusps is a generalized Kummer surface. In this paper we study several
configurations of nine cusps on the same K3 surface, which is the double cover of the plane
ramified on a sextic with nine cusps. We get the new configurations by studying conics through
the singular points of the sextic. The aim of the construction is to investigate the following
question: is it possible that the K3 surface is the generalized Kummer surface associated to two
non-isomorphic abelian surfaces ? This is a joint work with D. Kohl and X. Roulleau.
Holomorphic one forms on projective surfaces and applications
Sara Torelli, sara.torelli7@gmail.com
University of Hannover, Germany
In the talk I present a result, recently proven in collaboration with F.Favale and G.P.Pirola, that
aims to recover holomorphic 1-forms on smooth projective surfaces from divisors contracted
to points by big and semiample line bundles. I’ll then discuss its application to investigate
holomorphic forms on higher dimensional varieties (e.g. the moduli space of pointed curves
Mg,n) and related open problems.
105
