Generalized toric varieties, LVMB manifolds and Lie groupoids

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Author(s):	Matheus Silva Costa Total Authors: 1
Document type:	Doctoral Thesis
Press:	Campinas, SP.
Institution:	Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:	2022-02-04
Examining board members:	Lino Anderson da Silva Grama; Viviana Jorgelina Del Barco; Ricardo Miranda Martins; Josiney Alves de Souza; Mathieu Molitor
Advisor:	Lino Anderson da Silva Grama
Abstract
The aim of this work is to study generalized toric varieties, by exploring the relationship between toric orbifolds and quasifolds, on one side, and Lie groupoids, on the other. We present a general construction that uses the mathematical framework of LVMB manifolds to relate simultaneously toric varieties, orbifolds and quasifolds, to Lie groupoids. As an application of our construction we associate to Lie groupoids a family of varieties that include CP d and some of its orbifold and quasifold variants. As another application, we associate to Lie grupoids a family of varieties that include Hirzerbruch surfaces and some of its orbifold and quasifold variants (AU)

FAPESP's process:	17/03675-0 - Topics in symplectic geometry and applications to mirror symmetry
Grantee:	Matheus Silva Costa
Support Opportunities:	Scholarships in Brazil - Doctorate