Stable vector bundles on Pn, cohomology of monads and quiver representations.

• Grant number: 11/21398-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2012
• End date: March 31, 2015
• 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

Abstract

Our goal in this work is to continue the Ph.D. work where we proved results about simplicity of certain vector bundles on Pn using their relation with the Kronecker quiver. We also proved how to construct simple vector bundles on Pn of rank n with any linear homological dimension. Now we want to study the stability of these bundles. Besides we want to study other class of bundles that we did not approach in the Ph.D., like monads cohomology.

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)

MARCHESI, SIMONE; PRATA, DANIELA MOURA. Simplicity and exceptionality of syzygy bundles over P-n. Annali di Matematica Pura ed Applicata, v. 195, n. 1, p. 41-58, FEB 2016. (11/21398-7, 12/07481-1)

JARDIM, MARCOS; MENET, GREGOIRE; PRATA, DANIELA M.; SA EARP, HENRIQUE N.. Holomorphic bundles for higher dimensional gauge theory. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. 49, n. 1, p. 117-132, FEB 2017. (14/05733-9, 11/21398-7, 14/14743-8, 14/24727-0, 09/10067-0)