# Workshop on Algebraic Surfaces 2013

## Workshop on Algebraic surfaces

October 2, 2013, 10:00 - 17:00 at Leibniz Universität Hannover

Room: F442, Welfenschloss (university main building) - directions

## Talks

10:00 - 11:00  Tomasz Szemberg (PU Krakow) - The effect of points fattening on surfaces.

Following the ideas introduced by Bocci and Chiantini in case of the projective plane, we investigate the effect of points fattening on other types of surfaces, formulate a general framework for this kind of problems and finally state a conjecture governing the effect of linear subspaces fattening in higher dimensional situation. This report on a joint work with many collaborators.

11:30 - 12:30  Víctor González Alonso (UPC Barcelona/LUH) - On a conjecture of Xiao

(Abstract)

14:15 - 15:15  Remke Kloosterman (HU Berlin) - Applying Noether-Lefschetz theory to singular threefolds

We discuss how the techniques used to prove explicit Noether-Lefschetz type theorems can be adapted to study singular threefolds. More concretely, fix integers $2\leq d_1\leq \dots \leq d_c$ such that $d_c>\sum_{i=1}^{c-1} d_i$ holds. Then we describe the maximal dimensional family of complete intersection threefolds of multidegree $(d_1,\dots,d_c)$ which are not $\mathbb{Q}$-factorial. This proves a conjecture of Cynk and Rams.

15:45 - 16:45  Christian Liedtke (TU München) - Supersingular K3 Surfaces are Unirational

We show that supersingular K3 surfaces are related by purely inseparable isogenies. As an application, we deduce that they are unirational, which confirms conjectures of Artin, Rudakov, Shafarevich, and Shioda. The main ingredient in the proof is to use the formal Brauer group of a Jacobian elliptically fibered supersingular K3 surface to construct a family of "moving torsors" under this fibration that eventually relates supersingular K3 surfaces of different Artin invariants by purely inseparable isogenies. If time permits, we will show how these "moving torsors"  exhibit the moduli space of rigidified supersingular K3 crystals as an iterated projective bundle over a finite field.

## Fineprint

There is no formal registration; if you want to participate and need any assistance, you are welcome to contact Ute Szameitat at sekretariat-c with the usual ending math.uni-hannover.de.

Supported by ERC StG "SURFARI"

Organiser: Matthias Schütt