A categorical invariant for geometrically rational surfaces with a conic bundle structure

TL;DR

This paper introduces a new categorical invariant for minimal geometrically rational surfaces with conic bundle structures, expanding the tools for understanding their birational properties.

Contribution

It defines a categorical birational invariant for these surfaces using semiorthogonal decompositions, extending known results from del Pezzo surfaces.

Findings

Provides a categorical invariant for geometrically rational surfaces

Extends known invariants from del Pezzo surfaces

Enhances understanding of birational classifications

Abstract

We define a categorical birational invariant for minimal geometrically rational surfaces with a conic bundle structure over a perfect field via components of a natural semiorthogonal decomposition. Together with the similar known result on del Pezzo surfaces, this provides a categorical birational invariant for geometrically rational surfaces.