Hyperplane arrangements, foliations and Kronecker modules

• Grant number: 19/08279-0
• Support Opportunities: Regular Research Grants
• Duration: July 01, 2019 - September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Simone Marchesi
• Grantee: Simone Marchesi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project focuses on the study of vector bundles on smooth projective varieties.\\The first topic of research consists in the definition and the study of the concept of \textit{Kronecker Module} for instanton bundles on Flag varieties. This definition will help us understand better the jumping conic locus and their moduli spaces.\\The second topic of research focuses on the study and classification of foliations on projective spaces.\\The third topic of research leads with the study of hyperplane arrangements in the projective space, and in particular the study of the reflexive sheaves associated to them. (AU)