Hilbert functions of Cox rings of del Pezzo surfaces

Jinhyung Park, Joonyeong Won

Research output: Contribution to journalArticlepeer-review


To study syzygies of the Cox rings of del Pezzo surfaces, we calculate important syzygetic invariants such as the Hilbert functions, the Green–Lazarsfeld indices, the projective dimensions, and the Castelnuovo–Mumford regularities. Using these computations as well as the natural multigrading structures by the Picard groups of del Pezzo surfaces and Weyl group actions on Picard lattices, we determine the Betti diagrams of the Cox rings of del Pezzo surfaces of degree at most four.

Original languageEnglish
Pages (from-to)309-331
Number of pages23
JournalJournal of Algebra
StatePublished - 15 Jun 2017

Bibliographical note

Funding Information:
The second author has been supported by the National Research Foundation of Korea (NRF-2014R1A1A2056432) and IBS-R003-D1.

Publisher Copyright:
© 2017 Elsevier Inc.


  • Cox ring
  • Del Pezzo surface
  • Hilbert function
  • Syzygy


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