Page 106 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 106
ARITHMETIC AND GEOMETRY OF ALGEBRAIC SURFACES (MS-45)
On a family of surfaces with pg = q = 2 and K2 = 7
Matteo Penegini, penegini@dima.unige.it
Università di Genova, Italy
Coauthor: Roberto Pignatelli
In this talk we shall study a family of surfaces of general type with pg = q = 2 and K2 = 7,
originally constructed by C. Rito. We provide an alternative construction of these surfaces, that
allows us to describe their Albanese map and the corresponding locus M in the moduli space
of the surfaces of general type. In particular we prove that M is an irreducible component, two
dimensional and generically smooth.
New families of surfaces with canonical map of high degree
Roberto Pignatelli, Roberto.Pignatelli@unitn.it
University of Trento, Italy
Coauthor: Federico Fallucca
By a celebrated result of A. Beauville, if the dimension of the image of the canonical map of a
complex surface is two, then the image is either of genus zero or a canonical surface. In both
cases the degree of the map is uniformely bounded from above.
Until a few years ago, very few examples of surfaces with canonical map of high degree
were known.
Thanks to the work of some collegues, new examples have been obtained in recent years,
opening up new research questions and perspectives.
In this seminar we will present a new method for constructing surfaces with canonical map
of high degree and some new examples produced with this method.
Finally, we will discuss the contribution our examples make to the aforementioned issues.
Diagonal double Kodaira fibrations with minimal signature
Francesco Polizzi, francesco.polizzi@unical.it
Università della Calabria, Italy
We study some special systems of generators on finite groups, introduced in previous work
by the first author and called diagonal double Kodaira structures, in order to investigate non-
abelian, finite quotients of the pure braid group on two strands P2(Σb), where Σb is a closed
Riemann surface of genus b. In particular, we prove that, if G admits a diagonal double Kodaira
structure, then |G| ≥ 32, and equality holds if and only if G is extra-special. In the last part, as
a geometrical application of our algebraic results, we construct two 3-dimensional families of
double Kodaira fibrations having signature 16.
This is joint work with P. Sabatino.
104
On a family of surfaces with pg = q = 2 and K2 = 7
Matteo Penegini, penegini@dima.unige.it
Università di Genova, Italy
Coauthor: Roberto Pignatelli
In this talk we shall study a family of surfaces of general type with pg = q = 2 and K2 = 7,
originally constructed by C. Rito. We provide an alternative construction of these surfaces, that
allows us to describe their Albanese map and the corresponding locus M in the moduli space
of the surfaces of general type. In particular we prove that M is an irreducible component, two
dimensional and generically smooth.
New families of surfaces with canonical map of high degree
Roberto Pignatelli, Roberto.Pignatelli@unitn.it
University of Trento, Italy
Coauthor: Federico Fallucca
By a celebrated result of A. Beauville, if the dimension of the image of the canonical map of a
complex surface is two, then the image is either of genus zero or a canonical surface. In both
cases the degree of the map is uniformely bounded from above.
Until a few years ago, very few examples of surfaces with canonical map of high degree
were known.
Thanks to the work of some collegues, new examples have been obtained in recent years,
opening up new research questions and perspectives.
In this seminar we will present a new method for constructing surfaces with canonical map
of high degree and some new examples produced with this method.
Finally, we will discuss the contribution our examples make to the aforementioned issues.
Diagonal double Kodaira fibrations with minimal signature
Francesco Polizzi, francesco.polizzi@unical.it
Università della Calabria, Italy
We study some special systems of generators on finite groups, introduced in previous work
by the first author and called diagonal double Kodaira structures, in order to investigate non-
abelian, finite quotients of the pure braid group on two strands P2(Σb), where Σb is a closed
Riemann surface of genus b. In particular, we prove that, if G admits a diagonal double Kodaira
structure, then |G| ≥ 32, and equality holds if and only if G is extra-special. In the last part, as
a geometrical application of our algebraic results, we construct two 3-dimensional families of
double Kodaira fibrations having signature 16.
This is joint work with P. Sabatino.
104
