Del Pezzo Surfaces of degree 6 over an arbitrary field

TL;DR

This paper characterizes all degree 6 del Pezzo surfaces over any field using separable algebras, and applies this to compute their K-theory and derive an index reduction formula.

Contribution

It provides a complete characterization of degree 6 del Pezzo surfaces over arbitrary fields and links their structure to algebraic K-theory computations.

Findings

Characterization of del Pezzo surfaces via separable algebras

Computation of Quillen K-theory for these surfaces

Derivation of an index reduction formula for the surface's function field

Abstract

We give a characterization of all del Pezzo surfaces of degree 6 over an arbitrary field $F$. A surface is determined by a pair of separable algebras. These algebras are used to compute the Quillen $K$-theory of the surface. As a consequence, we obtain an index reduction formula for the function field of the surface.