On universal Severi varieties of low genus K3 surfaces

TL;DR

This paper proves the irreducibility of universal Severi varieties for certain low genus K3 surfaces, advancing understanding of their geometric properties.

Contribution

It establishes the irreducibility of universal Severi varieties for primitive K3 surfaces with genus between 3 and 11, excluding 10.

Findings

Universal Severi varieties are irreducible for g between 3 and 11, g ≠ 10.

The result applies to hyperplane sections of primitive K3 surfaces.

This advances knowledge of the geometry of K3 surfaces and their moduli.

Abstract

We prove the irreducibility of universal Severi varieties parametrizing irreducible, reduced, nodal hyperplane sections of primitive K3 surfaces of genus g, with 3 \le g \le 11, g \neq 10.