Maps on singular varieties and invariants

• Grant number: 22/15458-1
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2023
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Bruna Orefice Okamoto
• Grantee: Bruna Orefice Okamoto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Bárbara Karolline de Lima Pereira ; Francisco Braun ; João Nivaldo Tomazella

Abstract

This project proposes the study of invariants related to germs of analytical varieties and their relationship with equisingularities of families of such germs. More specifically, let's consider $\Sigma$-singularities: defined as inverse images by applications of a variety $\Sigma$ in the target with the expected codimension and defines invariants such as the evanescent Euler characteristic and the polar multiplicities of such varieties to later study equisingularities in families. Also, let's consider holomorphic map germs $f:(X,0)\to(\C^p,0)$ to see the relationship between the invariants that can be related to such germs and what they can tell us about equisingularity. Furthermore, we intend to continue our work on injectivity of polynomial maps $f:\R^2\to\R^2$. (AU)