Vector bundles over projective spaces

• Grant number: 14/08306-4
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: August 01, 2014
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Charles Aparecido de Almeida
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 16/14376-0 - Reflexive and torsion free sheaves on projective spaces, BE.EP.DD

Abstract

In this project we will study vector bundles on algebraic varieties, especially projective spaces, hyperquadrics and grassmanians, through the structure of their cohomology rings. Our starting points are a firm knowledge of the few examples of indecomposable low rank bundles on projective spaces, and the recent work of Eisenbud and Schreyer. The goal are searching for new examples of indecomposable low rank bundles on the varieties mentioned above, as well as a obtaining a deeper understanding of Hartshornes conjecture about vector bundles on projective 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)

ALMEIDA, CHARLES; ANDRADE, ALINE V.. Lefschetz property and powers of linear forms in K[x, y, z]. FORUM MATHEMATICUM, v. 30, n. 4, p. 857-865, JUL 2018. (16/14376-0, 14/08306-4)

ALMEIDA, C.; JARDIM, M.; TIKHOMIROV, A. S.; TIKHOMIROV, S. A.. New moduli components of rank 2 bundles on projective space. SBORNIK MATHEMATICS, v. 212, n. 11, p. 1503-1552, NOV 1 2021. (16/14376-0, 14/08306-4, 18/21391-1, 16/03759-6)

Academic Publications

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

ALMEIDA, Charles Aparecido de. Geometria dos espaços de moduli de feixes sem torção em espaços projetivos. 2019. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.