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Logarithmic sheaves for complete intersection schemes

Grant number: 21/10550-4
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2022
Effective date (End): February 28, 2026
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Marcos Benevenuto Jardim
Grantee:Felipe César Freitas Monteiro
Home 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

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).

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