Notiziario Scientifico
Settimana dall'8 al 14 settembre 2014
Giovedì 11 settembre 2014
Giovedì 11 settembre 2014
Giovedì 11 settembre 2014
Giovedì 11 settembre 2014
Giovedì 11 settembre 2014
Venerdì 12 settembre 2014
Venerdì 12 settembre 2014
Venerdì 12 settembre 2014
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 9 del venerdì precedente la settimana di pubblicazione.
Ore 10:00, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 11:30, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 14:00, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 15:30, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 17:00, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 10:00, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 11:30, Aula 211, Università di Roma III
Seminario di Geometria
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.
Ore 14:00, Aula E
Discussione di tesi di dottorato
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