Equivariant intersection cohomology of projective group embeddings

Acronym

P_EICPE

Consortium Coordinator

Gonzales Vilcarromero, Richard Paul

Start Date

2018

End Date

2019

Status

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

Description

The purpose of this project is to investigate and describe the equivariant intersection cohomology of possibly singular projective equivariant embeddings of reductive groups. Such a description is only available in the case of equivariant compactifications of tori, i.e. toric varieties, by work of Barthel, Brasselet, Fieseler and Kaup. Our goal is to extend their results to more general group embeddings, and to write down, explicitly and combinatorially, the equivariant intersection cohomology of possibly singular projective group embeddings, without placing any assumptions on the singular locus. Crucial to our description is the fact that all of these embeddings can be realized as projectivizations of affine monoids. In this setting, we anticipate that a suitable extension of GKM theory for the equivariant intersection cohomology of singular varieties with torus actions could lead to our main results. This is a further step in the program started in [G2]. The outcome should reveal certain aspects of the geometry of projective group embeddings which are not captured by equivariant bivariant theories.

Keywords

Cohomología de intersección

;

Geometría algebraica

;

Acciones de grupos

;

Variedades proyectivas

Área de conocimiento

Natural sciences

Campo OCDE

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