Cox rings of surfaces and the anticanonical Iitaka dimension
Michela Artebani, Antonio Laface
TL;DR
This paper explores how the finite generation of Cox rings for smooth projective surfaces relates to their anticanonical Iitaka dimension, providing insights into algebraic and geometric properties.
Contribution
It establishes a connection between Cox ring finite generation and the anticanonical Iitaka dimension for surfaces, advancing understanding in algebraic geometry.
Findings
Finite generation of Cox rings correlates with specific Iitaka dimensions.
Characterization of surfaces based on Cox ring properties.
New criteria for Cox ring finite generation in relation to anticanonical divisors.
Abstract
In this paper we investigate the relation between the finite generation of the Cox ring R(X) of a smooth projective surface X and its anticanonical Iitaka dimension k(-K_X).
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications