Virtual resolutions for a product of projective spaces

Christine Berkesch, Daniel Erman, Gregory G. Smith

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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 super uous summands. In this paper, we construct some much shorter free complexes that better encode the geometry.

Original languageEnglish (US)
Pages (from-to)460-481
Number of pages22
JournalAlgebraic Geometry
Issue number4
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© Foundation Compositio Mathematica 2020.


  • Deformation theory
  • Free resolutions
  • Toric varieties
  • Vector bundles


Dive into the research topics of 'Virtual resolutions for a product of projective spaces'. Together they form a unique fingerprint.

Cite this