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Moduli spaces of stable objects on the projective space

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

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Scientific publications (4)
(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)
FRANCO, EMILIO; JARDIM, MARCOS; MENET, GREGOIRE. Brane involutions on irreducible holomorphic symplectic manifolds. KYOTO JOURNAL OF MATHEMATICS, v. 59, n. 1, p. 195-235, . (14/05733-9, 15/06696-2, 12/16356-6, 16/03759-6)
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, . (14/23594-6, 14/14743-8, 16/03759-6, 15/20841-5)
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, . (16/14376-0, 14/08306-4, 18/21391-1, 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, . (14/14743-8, 16/03759-6)

Please report errors in scientific publications list by writing to: cdi@fapesp.br.