Virtual resolutions for a product of projective spaces

By Christine Berkesch Zamaere, Daniel Erman, Gregory G. Smith. Algebraic Geometry, 2017

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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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/411f9f3dfa0f4c62e2b2792df87257f786769059