Cox-Gorenstein algebras
Ugo Bruzzo, Rodrigo Gondim, Rafael Holanda, William D. Montoya
TL;DR
This paper investigates G-graded Artinian algebras with Poincaré duality, exploring their Lefschetz properties, establishing a correspondence with toric geometry, and introducing a Hessian criterion in the G-graded context.
Contribution
It introduces a new correspondence between toric and G-graded algebras and develops a Hessian criterion for Lefschetz properties in this setting.
Findings
Established a correspondence between toric and G-graded algebras.
Proved a Hessian criterion for Lefschetz properties in G-graded algebras.
Applied results to toric geometry contexts.
Abstract
We study G-graded Artinian algebras having Poincar\'e duality, considering in particular their Lefschetz properties. We also prove a correspondence between the toric setup and the G-graded one, provide an application to toric geometry, and prove a Hessian criterion in the G-graded setup
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications