Geometry of irreducible symplectic varieties

• Grant number: 14/05733-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2014
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Grégoire Menet
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Hyperkähler manifolds play a crucial role in Mathematics and Physics. They appear for instance in General Relativity as solutions spaces of Einstein equations, or in Quantum Field Theory in the study of Yang--Mills equations.One of the goals of the current project is the development of the theory of singular irreducible symplectic varieties (which could be seen as the singular case of hyperkähler manifolds). In particular we expect important improvements of this theory from the study of the Beauville--Bogomolov form and the periodic map.Another important aspect of hyperkähler geometry is the study of moduli spaces of semistable sheaves on hyperkähler manifolds. We hope to produce new examples of irreducible symplectic varieties by studying moduli spaces of sheaves, like Quot schemes, on K3 surfaces. (AU)

Scientific publications

(8)

(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)

KAPFER, SIMON; MENET, GREGOIRE. Integral cohomology of the generalized Kummer fourfold. ALGEBRAIC GEOMETRY, v. 5, n. 5, p. 523-567, SEP 2018. (14/05733-9)

MENET, GREGOIRE. On the integral cohomology of quotients of manifolds by cyclic groups. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 119, p. 280-325, NOV 2018. (14/05733-9)

FU, LIE; MENET, GREGOIRE. On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four. MATHEMATISCHE ZEITSCHRIFT, v. 299, n. 1-2, p. 203-231, OCT 2021. (14/05733-9)

MENET, GREGOIRE. Integral cohomology of quotients via toric geometry. EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, v. 6, p. 49-pg., 2022-02-23. (14/05733-9)

FU, LIE; MENET, GREGOIRE. On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four. MATHEMATISCHE ZEITSCHRIFT, JAN 2021. (14/05733-9)

FRANCO, EMILIO; JARDIM, MARCOS; MENET, GREGOIRE. Brane involutions on irreducible holomorphic symplectic manifolds. KYOTO JOURNAL OF MATHEMATICS, v. 59, n. 1, p. 195-235, APR 2019. (14/05733-9, 15/06696-2, 12/16356-6, 16/03759-6)

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)

MENET, GREGOIRE; NORDSTROM, JOHANNES; EARP, HENRIQUE N. SA. Construction of G(2)-instantons via twisted connected sums. MATHEMATICAL RESEARCH LETTERS, v. 28, n. 2, p. 471-509, 2021. (14/05733-9, 14/24727-0)