Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics

TL;DR

This paper explores the relationship between hyperelliptic curves, Clifford algebras, and complete intersections of two quadrics to describe and construct minimal rank Ulrich bundles.

Contribution

It introduces a novel approach linking hyperelliptic curves and Clifford algebras to explicitly construct Ulrich bundles on complete intersections of quadrics.

Findings

Describes Ulrich bundles on the intersection of two quadrics.

Constructs some of the minimal possible rank Ulrich bundles.

Establishes a connection between hyperelliptic curves and algebraic vector bundles.

Abstract

Using the connection between hyperelliptic curves, Clifford algebras, and complete intersections $X$ of two quadrics, we describe Ulrich bundles on $X$ and construct some of minimal possible rank.