Birational geometry of Beauville-Mukai systems II: general theory in low ranks

TL;DR

This paper investigates the birational geometry of Beauville-Mukai systems on K3 surfaces with Picard rank one, focusing on wall-crossing phenomena and providing a detailed analysis for rank two systems at low genus.

Contribution

It introduces a comprehensive description of the birational geometry of Beauville-Mukai systems, highlighting the presence of certain walls in the movable cones and analyzing rank two cases.

Findings

Identification of always-present walls in the movable cones.

Complete description of rank two systems for small genus.

Insights into the birational transformations of these systems.

Abstract

Via wall-crossing, we study the birational geometry of Beauville-Mukai systems on K3 surfaces with Picard rank one. We show that there is a class of walls which are always present in the movable cones of Beauville-Mukai systems. We give a complete description of the birational geometry of rank two Beauville-Mukai systems when the genus of the surface is small.