25 years ago Vafa and Witten predicted generating functions for the Euler numbers of the moduli spaces of sheaves on algebraic surfaces. In this talk, I review joint work with Martijn Kool to interpret and check these predictions in terms of virtual…
Categoria evento: Algebraic and Arithmetic Geometry Seminar
On the motive of zero-dimensional Quot schemes on a curve – Barbara Fantechi (SISSA, Trieste)
This is a report on joint work with Bagnarol and Perroni, available at arxiv:1907.00826. For any locally free coherent sheaf on a fixed smooth projective curve, we study the class, in the Grothendieck ring of varieties, of the Quot scheme that…
Smoothing of a reducible $I$-surface – Sönke Rollenske (Philipps-Universität Marburg)
The moduli space of stable surfaces is a modular compactification of the Gieseker moduli space of (canonical models of) surfaces of general type but has components consisting solely of non-smoothable surfaces. I will construct a smoothing of a…
Constructing $T$-singular surfaces – Julie Rana (Lawrence University)
Semi-log-canonical surfaces with ample canonical divisors are called stable. Their moduli space is a natural compactification (the KSBA compactification) of the Gieseker moduli space of canonical models of surfaces of general type. Among the…
Crystalline fundamental group and Berthelot’s conjecture for isocrystals – Fabio Tonini (Università di Firenze)
In the talk I will introduce the crystalline site of a variety in positive characteristic, discuss the notion of crystals and isocrystals over it and define its crystalline fundamental group. I will then discuss Berthelot’s conjecture and its…
The universal affine extension of an abelian variety – Michel Brion (Université Grenoble Alpes)
Every abelian variety $A$ over a field $k$ admits a universal extension by an affine $k$-group scheme. The talk will present a construction of this universal affine extension (first due to Serre when $k$ is algebraically closed of characteristic…
Supports of the Hitchin fibration on the reduced locus – Luca Migliorini (University of Bologna)
I’ll discuss some work in progress in collaboration with M.A. de Cataldo and J. Heinloth. Let $C$ be a nonsingular projective curve of genus $> 1$, and let $n$ and $d$ be two coprime integers. Given the moduli space $\mathcal{M}$ of stable Higgs…
Vector bundles on Fano threefolds and $K3$ surfaces – Arnaud Beauville (Université Côte d’Azur, Nice)
Let $X$ be a Fano threefold, and let $S$ be a smooth anticanonical surface (hence a $K3$) lying in $X$. Any moduli space of simple vector bundles on $S$ carries a holomorphic symplectic structure. Following an idea of Tyurin, I will show that in…