Computing higher direct images in Macaulay2

2025/05/28 by Zotine, Sasha
#13-04 (Primary) #14F08 #14M25 (Secondary) #14Q15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.22835

Abstract

This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms.

Citations

• Reduced Čech complexes and computing higher direct images under toric maps
• King's Conjecture and the Cox category
• A characterization of toric varieties in characteristic p
• Relative Beilinson Monad and Direct Image for Families of Coherent Sheaves
• Derived Categories of Toric Varieties

Related

• Reduced Čech complexes and computing higher direct images under toric maps
• A Step towards Computational Derived Algebraic Geometry: The RepHomology Package For Macaulay2
• Stabilization of direct images for curves
• Tate Resolutions on Products of Projective Spaces: Cohomology and Direct Image Complexes
• QuiversToricVarieties: a package to construct quivers of sections on complete toric varieties