Notiziario Scientifico

Settimana dall'8 al 14 settembre 2014


Giovedì 11 settembre 2014
Ore 10:00, Aula 211, Università di Roma III
Seminario di Geometria
Angela Ortega (Humboldt-Universitat, Berlino)
Prym map of degree-7 cyclic coverings
Giving a finite map between smooth coverings one can associate to it a polarized abelian variety, its Prym variety. This procedure induces the Prym map between the moduli space R_[p,g] of cyclic coverings of degree p over a genus g curve and the moduli of abelian varieties with some fixed polarization. There are exactly three cases when one can expect the Prym map to be generically finite, namely (p,g)=(2,6),(3,4),(7,2). In the case of double coverings of a genus 6 curve, R. Donagi proved that the fibers have the structure of the 27 lines on smooth cubic surface. C. Faber studied the case of triple cyclic coverings over a genus 4 curve and showed that Prym map is of degree 16. In this talk we will explain what is the corresponding picture for the remaining case of degree-7 cyclic coverings over a genus 2 curve. We will show that the Prym map is generically finite and can be extended to a proper map. We will also give a description of its image. This a joint work with Herbert Lange.


Giovedì 11 settembre 2014
Ore 11:30, Aula 211, Università di Roma III
Seminario di Geometria
Gavril Farkas (Humboldt-Universitat, Berlino)
What is the principally polarized abelian variety of dimension six?
The general principally polarized abelian variety of dimension at most five is known to be a Prym variety. This reduces the study of abelian varieties of small dimension to the beautifully concrete theory of algebraic curves. I will discuss recent progress on finding a structure theorem for principally polarized abelian varieties of dimension six, and the implications this uniformization result has on the geometry of their moduli space.


Giovedì 11 settembre 2014
Ore 14:00, Aula 211, Università di Roma III
Seminario di Geometria
Paola Frediani (Università di Pavia)
Totally geodesic submanifolds in the Torelli locus
We will describe recent results on totally geodesic submanifolds and Shimura subvarieties of A_g contained in the Torelli locus T_g. We will use the second fundamental form of the Torelli map to give an upper bound on the dimension of totally geodesic submanifolds contained in T_g, which depends on the gonality of the curve. We will then discuss some geometric properties of the second fundamental form of the Torelli map. We will finally describe some new examples of Shimura subvarieties in T_g obtained as non-abelian Galois coverings of P^1. These are results in collaboration with E. Colombo, A. Ghigi and M. Penegini.


Giovedì 11 settembre 2014
Ore 15:30, Aula 211, Università di Roma III
Seminario di Geometria
Antonio Rapagnetta (Università di Roma II)
Factoriality of 3-folds with isolated singularities
After a general introduction on factorility of algebraic varieties, I will concentrate on hypersurfaces of the 4-dimensional projective space admitting only isolated ordinary singularities (i.e. the projective tangent cone at a singular point is always smooth). I will give sufficient conditions for their factoriality and I will state a conjecture generalizing results on nodal hypersurfaces due to Ciliberto-Di Gennaro, Cheltsov and Kloosterman. This is a joint work with F.Polizzi and P.Sabatino.


Giovedì 11 settembre 2014
Ore 17:00, Aula 211, Università di Roma III
Seminario di Geometria
Giovanni Mongardi (Università di Milano)
Special K3 surfaces and their sheaves
Starting with a K3 surface with an automorphism of finite order, it is rather easy to produce automorphisms on (some) of its moduli spaces of stable sheaves. In this talk we give an answer to the converse: when is a manifold a moduli space of sheaves on a K3 and when are its automorphisms induced from those of the surface? Time permitting, we will discuss related results on lagrangian fibrations. This is joint work with Malte Wandel.


Venerdì 12 settembre 2014
Ore 10:00, Aula 211, Università di Roma III
Seminario di Geometria
Diego Matessi (Università di Milano)
On homological mirror symmetric of toric CY varieties
Mirror symmetry of Calabi-Yau varieties can be interpreted as a duality of Lagrangian torus fibrations. Using this approach I will describe the construction of lagrangian sections and spheres in the mirror of a toric Calabi-Yau. I will then illustrate a correspondence between sections and line bundles on the toric Calabi-Yau and between spheres and sheaves supported on the compact toric divisors. We expect that this correspondence will satisfy the properties of homological mirror symmetry.


Venerdì 12 settembre 2014
Ore 11:30, Aula 211, Università di Roma III
Seminario di Geometria
Paolo Stellari (Università di Milano)
Bridgeland stability on abelian and CY threefolds
We produce examples of stability conditions on the bounded derived category of coherent sheaves of any abelian threefold. This extends (with a completely different proof) results of Maciocia-Piyaratne for abelian threefolds. As a consequence we provide the first examples of stability conditions for smooth projective Calabi-Yau manifold answering a long standing question. This is a joint work with A. Bayer and E. Macrì.


Venerdì 12 settembre 2014
Ore 14:00, Aula E
Discussione di tesi di dottorato
Giuseppe Pipoli (Università di Roma I)
Mean Curvature flow of pinched submanifolds in positively curved symmetric spaces


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