Instanton sheaves on projective schemes

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.