## Geometry Seminar - Abstracts

### Talk

Thursday 17 January 2019, 16:00-17:00 in HG00.310

**Otto Overkamp** (Hannover)

*Kulikov models of Kummer surfaces*

### Abstract

Let \(K\) be a complete discrete valuation field with algebraically
closed residue field \(k\); we assume that the characteristic of \(k\)
is different from \(2\). Let \(X\) be a K3 surface over \(K\), i.e. a smooth,
projective, and geometrically integral algebraic surface over \(K\)
with trivial canonical sheaf and trivial \(H^1(X, \mathcal O_X)\).
In general, it is an open question whether we can find a finite
extension of \(K \) such that there exists a semistable model of \(X\)
over the ring of integers of that finite extension, even if we allow
the model to be an algebraic space rather than a scheme. I shall
explain how the question can be answered affirmatively if \(X\) is the
Kummer surface associated with some Abelian surface over \(K\). In
fact, we can even show that the models we construct are schemes, and
that their relative canonical sheaf vanishes (i.e., the models we
construct are so-called Kulikov models).
Time permitting, I shall say a few words about the general theory of Kulikov
models.

(

Back to geometry seminar schedule)