Bulletin of the London Mathematical Society· 2026Q1
Weighted veronese rings via convex semigroups
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- Q1SCImago
- 2026year
Short summary
This paper characterizes weighted Veronese rings and two-dimensional normal affine semigroup rings, detailing their determinantal presentations, Gröbner bases, Hilbert series, Betti numbers, and Koszul property.
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Key points
- Characterizes weighted Veronese rings and 2D normal affine semigroup rings.
- Determines determinantal presentations, Gröbner bases, Hilbert series, and Betti numbers.
- Investigates the structure of associated graded rings and the Koszul property.
- Provides higher-dimensional examples where these properties fail.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics