Sheaves on projective varieties and representations of quivers

• Grant number: 11/01071-3
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2012
• End date: June 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In the past 5 years I have worked on algebraic geometry, particularly on problemas involving certain classes of vector bundles on projective varieties. This is a very traditional topic of research within algebraic geometry, with profound connections with other areas of mathematics and mathematical physics. Recently, the study of vector bundles on projective varieties is influenced by other topics like representation theory and homological algebra. My research follows this tendency, and the research projects here presented go deeper into this path. Below five ongoing research projects in colaboration with mathematicians in Brazil and abroad, are briefly described. Moreover, the project of two of my PhD students are also discussed. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS; MARTINS, RENATO VIDAL. ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES. Glasgow Mathematical Journal, v. 57, n. 2, p. 285-321, MAY 2015. (11/01071-3, 09/12576-9)

JARDIM, MARCOS; VERBITSKY, MISHA. Trihyperkahler reduction and instanton bundles on CP3. COMPOSITIO MATHEMATICA, v. 150, n. 11, p. 1836-1868, NOV 2014. (11/01071-3, 09/12576-9)

HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS. Monad constructions of omalous bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 74, p. 36-42, DEC 2013. (11/01071-3, 09/18249-0)