Generalized instanton bundles on smooth projective varieties

• Grant number: 14/00498-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: April 19, 2014
• End date: July 18, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Helena Isabel Ferreira Soares
• Visiting researcher institution: Instituto Universitário de Lisboa (ISCTE-IUL), Portugal
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The main goal of this project is to study monads on nonsingular projective varieties. We intend to address this theme in two different directions. The first one will be developped in collaboration with the members Gauge Theory and Algebraic Geometry research group (Marcos Jardim, Simone Marchesi, Daniela Prata e Henrique Sá Earp). In this part of the project we will study monads on odd dimensional projective spaces, whose cohomology bundles are called generalized instanton bundles. In particular, we would like to determine when these bundles are simple or stable, their geometric structure and cohomological characterization. Furthermore, we will look for ways to such monads for other nonsingular projective varieties. The second direction, which also involves Pedro Macias Marques from the University of Évora (Portugal), deals with monads on Segre varieties. We will study existence of such monads, and determine whether their cohomology bundles are simple or stable, and study their moduli spaces. (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)

MARCHESI, SIMONE; MARQUES, PEDRO MACIAS; SOARES, HELENA. MONADS ON PROJECTIVE VARIETIES. PACIFIC JOURNAL OF MATHEMATICS, v. 296, n. 1, p. 155-180, SEP 2018. (14/12558-9, 14/00498-1, 17/03487-9)