Variations in multiplicities and limited polynomials

• Grant number: 15/08149-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2015
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo Jose Saia
• Grantee: Maria Jadwiga Michalska
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

This work addresses issues in two research lines of the Thematic project in Singularity Theory: Geometry and classification of singularities and Topology sets and singular maps, one investigates jumps of multiplicities of ideals and inserts in the study of relationships between invariants of singularities of map germs and multiplicities of ideals and modules, this issue is directly linked to the study of invariants of singularities and geometry of singular maps. Another issue concerns the application of methods of topology for the study of bounded polynomials. We emphasize the use of Newton filtrations as a tool in the determinacy of the integral closure of ideals, concept closely related with the multiplicity of ideals and also with Lojasiewicz-type inequalities, which are related with bounded polynomials.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MICHALSKA, MARIA; WALEWSKA, JUSTYNA. Milnor Numbers of Deformations of Semi-Quasi-Homogeneous Plane Curve Singularities. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 50, n. 1, p. 95-117, MAR 2019. (15/08149-9)