Moduli spaces of stable objects on the projective space

• Grant number: 16/03759-6
• Support Opportunities: Scholarships abroad - Research
• Start date: January 15, 2017
• End date: December 22, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Host Investigator: Antony Maciocia
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Edinburgh, Scotland

Abstract

The study of moduli spaces of sheaves is a classical and relevant problem in algebraic geometry. The concept of stability is an important issue in this area, and the use of different notions can lead to a deeper understanding of the geometry of the moduli space of the object being studied.The present research project focuses on instanton sheaves on the 3 dimensional projective space. These objects can be studied from three different points of view: as torsion free sheaves, as representations of a given quiver, and as objects in the derived category of coherent sheaves. We intend to develop each of the previous points of view, exploring the different notions of stability that appear in each of three categories mentioned: Gieseker stability in the category of coherent sheaves, King stability in the category of representations of quivers, and Bridgeland stability in the derived category of coherent sheaves.The central questions we hope to address are the connectedness of the moduli space of instanton sheaves, wall-crossing phenomena, and the characterization of possible degenerations of instanton sheaves in the different categories. We also hope to make progress on the description of moduli spaces of Bridgeland stable objects in derived category of coherent sheaves on the 3 dimensional projective space, which are still poorly understood in the literature.

Scientific publications

(5)

(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)

CALVO-ANDRADE, OMEGAR; CORREA, MAURICIO; JARDIM, MARCOS. Codimension One Holomorphic Distributions on the Projective Three-space. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. 2020, n. 23, p. 9011-9074, NOV 2020. (14/23594-6, 15/20841-5, 14/14743-8, 16/03759-6)

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; MAICAN, MARIO; TIKHOMIROV, ALEXANDER S.. MODULI SPACES OF RANK 2 INSTANTON SHEAVES ON THE PROJECTIVE SPACE. PACIFIC JOURNAL OF MATHEMATICS, v. 291, n. 2, p. 399-424, DEC 2017. (14/14743-8, 16/03759-6)

FRANCO, EMILIO; JARDIM, MARCOS. Mirror symmetry for Nahm branes. EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, v. 6, p. 29-pg., 2022-02-28. (12/16356-6, 16/03759-6, 18/21391-1)

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)