Logarithmic sheaves for complete intersection schemes

• Grant number: 21/10550-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2022
• End date: March 01, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Felipe César Freitas Monteiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/21391-1 - Gauge theory and algebraic geometry, AP.TEM
• Associated scholarship(s): 23/05784-1 - Logarithmic sheaves for complete intersection schemes, BE.EP.DR

Abstract

This project seeks to establish the study of logarithmic sheaves T_à over complete intersection schemes V(Ã), which are algebraic varieties given as the zero-set of a regular sequence à = {f_1, . . . , f_k} of homogeneous polynomials in the projective space of dimension n. These sheaves are defined as the kernel of the Jacobian morphism J_à = (f_1, . . . , f_k), generalizing the classical construction for k = 1, whereD = V (Ã) is a divisor and T_à is the vector bundle of logarithmic derivations over D (see [4]). Following the program of classification and characterization of particular cases, initiated in [5], this project is specially interested in stability aspects of associated moduli spaces and the relation between local freeness of T_à and geometrical properties of the variety V (Ã).