Toric varieties, vector fields, and Newton polyhedra

• Grant number: 24/22060-0
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2025
• End date: March 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Thais Maria Dalbelo
• Grantee: Thais Maria Dalbelo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Andres Daniel Duarte ; Fernando Lourenço ; Maria Elenice Rodrigues Hernandes ; Thiago Filipe da Silva

Abstract

This project is divided into three parts. In the first part, we will address the problem of classifying the phase portrait at infinity of planar vector fields under topological equivalence. In the second part, we intend to use properties and information from the relationship between determinantal varieties and toric geometry, such as the concept of Newton polyhedron, to investigate conditions that guarantee Whitney equisingularity for families of determinantal varieties. In the third part, we will study the properties of toric varieties, as well as the relationship between this class of varieties and determinantal varieties. (AU)