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arXiv · 2603.12441

Weighted Veronese Rings via Convex Semigroups

Bek Chase·Luca Fiorindo·Thiago Holleben·Emanuela Marangone·Thai Thanh Nguyen·Alexandra Seceleanu·Srishti Singh
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Abstract

We determine properties of two-dimensional normal affine semigroup rings, and in particular of weighted Veronese rings, including determinantal presentation, Gr\"obner 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.

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Bek Chase, Luca Fiorindo, Thiago Holleben, Emanuela Marangone, Thai Thanh Nguyen, Alexandra Seceleanu, Srishti Singh. 2026-03-12. Weighted Veronese Rings via Convex Semigroups. https://arxiv.org/abs/2603.12441

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