A survey on Cox rings
Antonio Laface, Mauricio Velasco
TL;DR
This survey reviews the construction of Cox rings for algebraic varieties and explores their role in understanding the birational geometry when these rings are finitely generated.
Contribution
It provides a comprehensive overview of Cox ring construction and examines their implications in the birational classification of algebraic varieties.
Findings
Cox rings can be finitely generated for certain classes of varieties.
Finitely generated Cox rings facilitate the study of birational geometry.
The survey highlights key open problems in Cox ring theory.
Abstract
We survey the construction of the Cox ring of an algebraic variety X and study the birational geometry of X when its Cox ring is finitely generated.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications