Program - December 18, 2019 (Aula C, second floor)
You can download the poster and the program.
9:30-10:20
Antonio Rapagnetta
The Hodge numbers of O'Grady's 10-dimensional irreducible symplectic manifold
Abstract:
I report on a joint work with M.A. de Cataldo and G. Sacca' where we determine the Hodge diamond of the ten dimensional irreducible symplectic manifold discovered by O'Grady.
10:30-11:20
Francesco Meazzini
On the Kaledin-Lehn formality conjecture
Abstract:
Kaledin-Lehn conjectured the formality for the DG-Lie algebra of derived endomorphisms of any polystable sheaf on a K3 surface.
The relevance of the formality conjecture relies in its consequences concerning the geometry of the moduli space of semistable sheaves on the K3.
The conjecture was proven after several contributions mainly due to Kaledin-Lehn themselves, Zhang, Yoshioka, Arbarello-Saccà, Budur-Zhang.
We propose an alternative algebraic approach to the problem, eventually proving that the formality conjecture holds on any smooth minimal projective surfaces of Kodaira dimension 0.
This is a joint work with R. Bandiera and M. Manetti.
12:00-12:50
Rosa Winter
Density of rational points on a family of del Pezzo surfaces of degree 1
Abstract:
Let S be a del Pezzo surface of degree 1 of the form y^2=x^3+Az^6+Bw^6 in the weighted projective space P_Q(2,3,1,1) with coordinates (x,y,z,w), with A,B nonzero. Let E be the elliptic surface obtained by blowing up the base point of the anticanonical linear system of S. In this talk I show that if S contains a rational point P=(x_0,y_0,z_0,w_0) with z_0,w_0 unequal to 0, and such that the corresponding point on E is non-torsion on its fiber, then the set of rational points on S is dense with respect to the Zariski topology. I will compare this result to previous results on density of rational points on del Pezzo surfaces. This is joint work with Julie Desjardins.