Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes

TL;DR

This paper introduces the Macaulay2 package TateOnProducts for computing cohomology, Beilinson monads, and direct image complexes of sheaves on products of projective spaces, facilitating advanced algebraic geometry calculations.

Contribution

The paper presents a new computational tool that automates complex cohomology and derived category computations for sheaves on product projective spaces.

Findings

Efficient computation of cohomology tables.

Automated derivation of Beilinson monads.

Calculation of direct image complexes under morphisms.

Abstract

We describe the Macaulay2 package TateOnProducts and its capabilities, which include computing cohomology tables and Beilinson monads of sheaves on products of projective spaces and the derived category pushForward of a sheaf under a morphism from a projective scheme to a projective space.