Weighted veronese rings via convex semigroups
Abstract We determine several properties of two‐dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentations, Gröbner bases, graded Hilbert series and graded Betti numbers, the structure of their associated graded rings, and their Koszul property. We give examples in higher dimensions illustrating that the first and last properties may fail. Our approach leverages convex monomial ideals as introduced in [16], which give rise to convex semigroups.
Authors
- Alexandra Seceleanu (ORCID: https://orcid.org/0000-0002-7929-5424)
- Emanuela Marangone (ORCID: https://orcid.org/0000-0003-4374-0714)
- Luca Fiorindo (ORCID: https://orcid.org/0000-0002-6435-0128)
- Thiago Holleben (ORCID: https://orcid.org/0009-0001-3669-6690)
- Bek Chase
- Thai Thanh Nguyen
- Srishti Singh
Institutions
- University of Nebraska–Lincoln (US)
- Mathematics Research Center (MX)
- University of Dayton (US)
- Knoxville College (US)
- University of Central Arkansas (US)
- Max Planck Institute for Mathematics in the Sciences (DE)
- Mathematics Research Center (MX)
- Hue University of Education (VN)
- University of Tennessee at Knoxville (US)
- University of Genoa (IT)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-10-27
- DOI
- https://doi.org/10.1112/blms.70536
- Primary Topic
- Commutative Algebra and Its Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- National Foundation for Science and Technology Development
- University of Nebraska-Lincoln
- University of Dayton
- Pacific Institute for the Mathematical Sciences
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- University of Central Arkansas
- University of Manitoba
- Dalhousie University
- Università degli Studi di Genova
- Đại học Huế
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
- Division of Mathematical Sciences