ACM sheaves of pure rank two on reducible hyperquadrics

TL;DR

This paper classifies certain rank-two sheaves on reducible hyperquadrics and demonstrates that such surfaces exhibit wild representation type, advancing understanding of their algebraic structure.

Contribution

It provides a classification of ACM sheaves of rank two on reducible hyperquadrics, revealing their complex representation type.

Findings

Classification of rank-two ACM sheaves on reducible hyperquadrics

Proof that reducible quadric surfaces are of wild type

Enhanced understanding of the algebraic complexity of these surfaces

Abstract

We classify a special type of arithmetically Cohen-Macaulay sheaves of rank two on reducible and reduced quadric hypersurfaces. As a consequence we show that a reducible and reduced quadric surface is of wild type.