Polynomial differential systems, toric varieties and Newton polyhedra.

• Grant number: 24/03660-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2024
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Nelson Amorim Júnior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

In this research project, we propose to study the results presented by Brunella and Miari in the article entitled Topological equivalence of a plane vector field with its principal part defined through Newton Polyhedra, as well as the tools necessary to obtain such results. In particular, we aim to explore the strong relationship between fields of non-degenerate vectors and toric varieties.