Representation Theory and Algebraic Geometry

• Grant number: 07/07469-3
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2008
• End date: February 29, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Daniela Moura Prata dos Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 05/04558-0 - Symmetries in geometry, topology and mathematical physics, AP.TEM

Abstract

In her masters work, Daniela Prata studied the relation between the category of representations of quivers and the category of twisted representations of quivers, proving that the category of twisted representations of a quiver is equivalent to the category of representations of another quiver which is easily constructed from the original one.In this project, we are interested to possible applications of twisted representations to the theory of vector bundles over algebraic varieties. Several important classes of vector bundles, like Steiner bundles or linear bundles, are closely related to twisted representations of certain quivers, which are in turn, as mentioned above, equivalent to usual representations of a diferent quiver. One can then apply well known results of the theory of representations of quivers to understand various properties of these bundles, like indecomposability, simplicity and stability.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SANTOS, Daniela Moura Prata dos. Representações de quivers e fibrados vetoriais sobre espaços projetivos. 2012. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.