Instanton sheaves on projective schemes

Abstract

A h–instanton sheaf on a closed subscheme X of some projective space endowed with an ample and globally generated line bundle OX(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.