Instanton sheaves on projective schemes

TL;DR

This paper explores the properties and classifications of $h$-instanton sheaves on various projective schemes, establishing connections with Ulrich sheaves and analyzing their behavior on different types of algebraic varieties.

Contribution

It introduces a comprehensive study of $h$-instanton sheaves, relating them to Ulrich sheaves and examining their structure on multiple classes of projective schemes.

Findings

Relation between $h$-instanton and Ulrich sheaves established

Characterization of $h$-instanton sheaves on curves and surfaces

Construction of monads for $h$-instanton bundles under certain conditions

Abstract

A $h$-instanton sheaf on a closed subscheme $X$ of some projective space endowed with an ample and globally generated line bundle $\mathcal{O}_X(h)$ is a coherent sheaf whose cohomology table has a certain prescribed shape. In this paper we deal with $h$-instanton sheaves relating them to Ulrich sheaves. Moreover, we study $h$-instanton sheaves on smooth curves and surfaces, cyclic $n$-folds, Fano $3$-folds and scrolls over arbitrary smooth curves. We also deal with a family of monads associated to $h$-instanton bundles on varieties satisfying some mild extra technical conditions.