Group embeddings and Cox rings

Acronym

P_GE-COX

Consortium Coordinator

Gonzales Vilcarromero, Richard Paul

Start Date

March 15, 2017

End Date

March 15, 2018

Status

https://purl.org/pe-repo/concytec/estadoProyecto#concluido

Tipo de proyecto

https://purl.org/pe-repo/ocde/tipoProyecto#investigacionBasica

Description

The purpose of this project is to investigate the cone of projective group embeddings with the same Cox ring R(X). The ring R(X) is a unique factorization domain. Q-factorial projective varieties with a finitely generated Cox ring are characterized using Mori theory. If X is a spherical variety, then R(X) is a finitely generated algebra, and it carries a natural grading by the classes of effective divisors. The Cox ring of spherical varieties has been described by Brion and Gagliardi. In the case when X is a G-embedding, we can associate a certain cone H, in the class group Cl(X), so that any element y of H defines a group embedding X_y satisfying R(X_y) = R(X). It seems that H corresponds to the movable cone of X. The purpose of this project is to calculate H explicitely, using the knowledge of NE(X), the cone of effective curves on X, and nef(X), the cone of numerically effective divisors on X, and certain monoid data. Moreover, we would like to understand, and quantify, how the cones H and H', associated to different G-embeddings, are related.

Keywords

Inmersiones de grupos

;

Anillos de Cox

;

Geometría algebraica

;

Teoría de grupos

Área de conocimiento

Natural sciences

Campo OCDE

https://purl.org/pe-repo/ocde/ford#1.01.01