Perverse coherent sheaves and Bridgeland Stability

• Grant number: 24/15918-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: February 10, 2025
• End date: December 25, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Renato Vidal da Silva Martins
• Visiting researcher institution: Instituto De Ciências Exatas/Icex/Ufmg, Brazil
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM

Abstract

We present here the plan of activities for Prof. Renato Vidal Martins' visit to IMECC-UNICAMP. This project is based on an extensive research plan with two central themes, namely, Perverse Instanton Sheaves and Bridgeland Stability, as well as, Clifford Index of Torsion-Free Sheaves, both to be developed with Prof. Marcos Jardim. The first concerns the restructuring and generalization of results obtained by both authors, on perverse instanton sheaves in previous articles, in terms of more general and advanced stability concepts. While the second deals with a recent connection found between Clifford indices, a central theme in curve theory, and Bridgeland stability, where such a technique can be used to obtain still open results on such invariant. The scientific plan also includes work with Prof. Ethan Cotterill, on the gonality of rational curves and Severi varieties. In addition, the professor intends to continue other ongoing projects, e.g., on Brill-Noether varieties and Green's Conjecture, with the aim of involving professors, researchers, and students of Algebraic Geometry at IMECC. The project also includes courses and lectures to be given by Prof. Renato Vidal Martins, as well as the organization and participation in various events. (AU)