Matthias Schütt

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math.AG2025

Miyaoka's bound for conics on K3 surfaces and beyond

SÅawomir Rams, Matthias SchÃ¼tt

We show that Miyaoka's bound for the number of conics on a degree-2h K3 surface is attained for high h, and analogously for higher even degree (smooth) rational curves.

math.AG2024

The 2-divisibility of divisors on K3 surfaces in characteristic 2

Toshiyuki Katsura, Shigeyuki KondÅ, Matthias SchÃ¼tt

We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n = 8, 12, 16, 20$ . More pr…

math.AG2024

Normal forms for quasi-elliptic Enriques surfaces and applications

Toshiyuki Katsura, Matthias SchÃ¼tt, Matthias Schütt

We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application i…

math.AG2024

Low degree rational curves on quasi-polarized K3 surfaces

SÅawomir Rams, Matthias SchÃ¼tt

We prove that there are at most $(24 - r_{0})$ low-degree rational curves on high-degree models of K3 surfaces with at most Du Val singularities, where $r_{0}$ is the number of exception…