Monads on projective varieties, syzygy bundles and Gorenstein Artin algebras

• Grant number: 14/12558-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 15, 2014
• End date: May 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Pedro Correia Goncalves Macias Marques
• Visiting researcher institution: Universidade de Évora , Portugal
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• City of the host institution: Campinas

Abstract

The research project has three main tasks: 1. to study monads on projective varieties, addressing their existence, whether they are stable sheaves, and if so study their moduli spaces; 2. to study the stability of sencond-order syzygies in the projective space; 3. to work on the conjecture of Bernardi and Ranestad on the cactus rank of a general cubic form. (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)

BERNARDI, ALESSANDRA; JELISIEJEW, JOACHIM; MARQUES, PEDRO MACIAS; RANESTAD, KRISTIAN. On polynomials with given Hilbert function and applications. COLLECTANEA MATHEMATICA, v. 69, n. 1, p. 39-64, JAN 2018. (14/12558-9)

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)