Centrosymmetric determinantal varieties: geometry, singularities, and topological invariants

• Grant number: 25/06726-0
• Support Opportunities: Scholarships abroad - Research
• Start date: September 01, 2026
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Leandro Nery de Oliveira
• Grantee: Leandro Nery de Oliveira
• Host Investigator: Juan Jose Nuno Ballesteros
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Universitat de València, Spain
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

This project focuses on the study of centrosymmetric determinantal varieties, obtained as loci of centrosymmetric matrices with bounded rank. The research will address their algebraic and topological properties - such as equidimensionality, irreducibility, and the Cohen-Macaulay condition, among others - as well as the structure of their singular loci. The study will also include refined invariants influenced by centrosymmetry, equisingularity conditions, and aspects of classification via moduli spaces. The proposal combines classical techniques from singularity theory with recent approaches motivated by the presence of centrosymmetry, aiming to broaden the geometric understanding of these varieties. In addition to its theoretical impact, this research seeks to establish a new line of investigation at UFSCar and to strengthen international collaborations, contributing to the advancement of singularity theory. (AU)