考克斯-哥伦布代数

arXiv - MATH - Commutative Algebra Pub Date : 2024-07-25 DOI:arxiv-2407.17811

Ugo Bruzzo, Rodrigo Gondim, Rafael Holanda, William D. Montoya

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引用次数: 0

摘要

本文是研究非标准梯度代数的第一步，研究了具有Poincar\'e 对偶性的非标准梯度代数及其 Lefschetz 性质。我们证明了 toric 设置和 G-graded 设置之间的等价性，推广了 Macaulay-Matlisduality，引入了 Lefschetz 性质，并证明了 G-graded 设置中的 Hessian 准则。我们证明了卡塔尼-科克斯-迪肯斯坦的 "标度一猜想 "的一个特例。

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Cox-Gorenstein algebras

This paper is a first step in the study of nonstandard graded algebras having Poincar\'e duality and their Lefschetz properties. We prove the equivalence between the toric setup and the G-graded one, generalize Macaulay-Matlis duality, introduce Lefschetz properties and prove a Hessian criteria in the G-graded setup. We prove a special case of the Codimension One Conjecture of Cattani-Cox-Dickenstein.

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arXiv - MATH - Commutative Algebra

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