Generalized toric varieties and mirror symmetry

• Grant number: 19/06355-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2019
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Lino Anderson da Silva Grama
• Grantee: Matheus Silva Costa
• Supervisor: Ludmil Katzarkov
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Miami, United States
• Associated to the scholarship: 17/03675-0 - Topics in symplectic geometry and applications to mirror symmetry, BP.DR

Abstract

Mirror symmetry has been extensively studied for toric varieties. In this project we intend to understand what is meant by generalized toric varieties, in particular we will study orbifolds, quasifolds, Lie groupoids, and LVMB manifolds in connection to certain construction procedures that come from the theory of toric varieties.We also aim to understand if it is possible to talk about generalized toric varieties in a unified language, and if results of toric variety mirror symmetry can be extended to the setting of generalized toric varieties. (AU)