Bundles on Pn with vanishing lower cohomologies

TL;DR

This paper investigates vector bundles on projective spaces with vanishing lower cohomologies, classifies their Hilbert functions, and describes the structure of their moduli spaces using stratifications and Betti numbers.

Contribution

It provides a comprehensive classification of such bundles based on Hilbert functions and describes the stratification of their moduli spaces via rational quotients and Betti number lattices.

Findings

Classification of Hilbert functions for bundles with vanishing lower cohomologies

Stratification of moduli spaces by rational quotients

Moduli space strata form a graded lattice based on Betti numbers

Abstract

We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathbf{M}$ according to the Hilbert function $H$ and classify all possible Hilbert functions $H$ of such bundles. For each $H$, we describe a stratification of $\mathbf{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.