Data:
13/01/2025 - 14:30 to 14/01/2025 - 13:00
Aula:
Aula S
Categoria:
Altri eventi
Descrizione:
Meeting of the algebraic geometry groups of Genova, Nice and Torino
13 ,14 January 2025, Palazzo Campana, aula S
Program:
Monday 13/1
14:30 15:30 Karl Christ (University of Torino)
15:45 16:45 Michele Ancona (University of Nice)
coffee break
17:30 18:30 Simone Billi (University of Genova)
Dinner at 20
Tuesday 13/1
9:00 - 10:00 Christian Pauly (University of Nice)
coffee break
10:40 11:40 Eleonora Romano (University of Genova)
11:50 12:50 Francesco Malaspina (Politecnico of Torino)
Titles & abstracts
Michele Ancona
Metric and spectral aspects of random plane curves
Any complex plane curve is endowed with a Riemannian metric induced by the ambient
Fubini Study metric of the complex projective plane. We give probabilistic lower bounds on
some metric and spectral quantities (such as the systole or the spectr al gap) of the plane curves
when these are chosen randomly in the Fubini Study ensemble. This is a joint work with
Damien Gayet.
Simone Billi:
Cubic fourfolds with an automorphism of prime order
The algebraic lattice of a cubic fourfold encodes much information about its geometry.
We classify the algebraic lattice of general cubic fourfolds admitting a prime order automorphism,
in these cases the lattice is generated by the square of a hyperplane class along with classes
of planes or cubic scrolls. Speculating on the rationality co njecture, we show that some of
these cubic fourfolds are rational but not equivariantly rational. As an application of the
classification, we study transformations of manifolds of OG10 type that are induced by prime
order automorphisms of cubic fourfolds v ia the (twisted) Laza Saccà Voisin construction.
Karl Christ:
Irreducibility of Severi varieties on toric surfaces
Severi varieties parametrize integral curves of fixed geometric genus in a given linear system
on a surface. In this talk, I will discuss t he classical question of whether Severi varieties are
irreducible and its relation to the irreducibility of other moduli spaces of curves. I will indicate
how tropical methods can be used to answer such irreducibility questions. The new results are from onfrom ongoing joint work with Xiang He and Ilya Tyomkin.going joint work with Xiang He and Ilya Tyomkin.
Francesco Malaspina
On different notions of instanton bundles on projective varietiesOn different notions of instanton bundles on projective varieties
The notion of instanton bundle over the projective space is important both in theoretical physics and in differential physics and in differential and algebraic geometry. Recently, using derived category and algebraic geometry. Recently, using derived category techniques, a notion of instanton bundle on Fano varieties with Picard number one has been techniques, a notion of instanton bundle on Fano varieties with Picard number one has been given by Faenzi and Kuznetsov. In the talk we will discuss how to extend this notion to any given by Faenzi and Kuznetsov. In the talk we will discuss how to extend this notion to any polarized projecpolarized projective variety. This is a joint work with Vincenzo Antonelli.tive variety. This is a joint work with Vincenzo Antonelli.
Christian Pauly
Hecke transformations for orthogonal and symplectic bundlesHecke transformations for orthogonal and symplectic bundles
Hecke transformations provide a powerful tool in the study of the geometry of moduli spaces of vector bundles over cuof vector bundles over curves. After defining Hecke transformations for vector bundles, I rves. After defining Hecke transformations for vector bundles, I will describe some classical applications (Tyurin's duality theorem, Narasimhanwill describe some classical applications (Tyurin's duality theorem, Narasimhan--Ramanan Ramanan theorem). Finally, I will consider orthogonal and symplectic vector bundles and introduce theorem). Finally, I will consider orthogonal and symplectic vector bundles and introduce some generalsome generalization of Hecke transformations in this setization of Hecke transformations in this set--up. This is joint work with Hacen up. This is joint work with Hacen Zelaci.Zelaci.
Eleonora Romano:
KK--polystability of Fano 4polystability of Fano 4--folds with large Lefschetz defectfolds with large Lefschetz defect
We discuss K--polystability of smooth complex Fano 4polystability of smooth complex Fano 4--folds having large Lefschetz defect, folds having large Lefschetz defect, tthat is greater or equal then 3, with a special focus on the case of Lefschetz defect 3. After hat is greater or equal then 3, with a special focus on the case of Lefschetz defect 3. After recalling the classification of Fano 4recalling the classification of Fano 4--folds having Lefschetz defect 3, we deduce that there folds having Lefschetz defect 3, we deduce that there are 5 Kare 5 K--polystable families (out of 19) among them. The results presepolystable families (out of 19) among them. The results presented in this talk are joint nted in this talk are joint works with C. Casagrande and S. Secci.works with C. Casagrande and S. Secci