Virtual Resolutions for a Product of Projective Spaces

Abstract

Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the geometry.

22 pages, 1 figure

References in corpus (1)

• Tate Resolutions for Products of Projective Spaces

Cited by in corpus (2)

• A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
• Linear Truncations Package for Macaulay2