Weighted Veronese Rings via Convex Semigroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911511550623744 |
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| author | Chase, Bek Fiorindo, Luca Holleben, Thiago Marangone, Emanuela Nguyen, Thai Thanh Seceleanu, Alexandra Singh, Srishti |
| author_facet | Chase, Bek Fiorindo, Luca Holleben, Thiago Marangone, Emanuela Nguyen, Thai Thanh Seceleanu, Alexandra Singh, Srishti |
| contents | We determine properties of two-dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentation, Gröbner basis, 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 Herzog-Qureshi-Saem(2019), which give rise to convex semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12441 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted Veronese Rings via Convex Semigroups Chase, Bek Fiorindo, Luca Holleben, Thiago Marangone, Emanuela Nguyen, Thai Thanh Seceleanu, Alexandra Singh, Srishti Commutative Algebra Algebraic Geometry 13A02 (Primary) 13A30, 13F65, 14M12, 16S36, 16S37 (Secondary) We determine properties of two-dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentation, Gröbner basis, 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 Herzog-Qureshi-Saem(2019), which give rise to convex semigroups. |
| title | Weighted Veronese Rings via Convex Semigroups |
| topic | Commutative Algebra Algebraic Geometry 13A02 (Primary) 13A30, 13F65, 14M12, 16S36, 16S37 (Secondary) |
| url | https://arxiv.org/abs/2603.12441 |