Methods of commutative algebra and algebraic geometry in singularity theory.

• Grant number: 16/08929-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: November 09, 2016
• End date: October 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Daniel Levcovitz
• Grantee: Daniel Levcovitz
• Visiting researcher: Aron Simis
• Visiting researcher institution: Universidade Federal de Pernambuco (UFPE). Centro de Ciências Exatas e da Natureza (CCEN) , Brazil
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

This project hinges on the impact of the fine theory of ideals in singularities. The informal designation ``fine theory'' refers to arithmetical and homological properties of ideals which lead to a deep intertwining with purely geometric properties of algebraic varieties and their classification. This cooperation naturally disembarks in singularity theory.Venturing facilitating the reader's insertion in the contents proper of the project, we divide it along the following general themes:1.Blowup methods2.Differential methods3.Birational methods (AU)