Chow group

• Grant number: 21/02970-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2021
• End date: May 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Michelle Ferreira Zanchetta Morgado
• Grantee: Lucas Pedro Martins
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

The study of Chow group serves as a basis for the theory of intersection in Algebraic Geometry, a very important and current tool in Theory of Singularities. Starting with the study of Scheme Theory, we consider varieties, which are finite type schemes over some algebraically closed field, formal linear combinations of them with integer coefficients called cycles and through the rational equivalence the Chow groups of this variety are defined. This project aims to describe these groups and their properties, the relationship between specific morphisms between varieties and homomorphisms between the associated Chow groups. Ending with the construction of bilinear applications associated with Chow groups of a variety X that corresponds geometrically to taking intersections of a divisor with a k-dimensional subvariety. Thus, knowing the Chow groups of a variety and the products from the previous intersection, Bézout-style results are achieved. (AU)