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Determinants, Even Instantons and Bridgeland Stability

Texto completo
Autor(es):
Pretti, Victor do Valle
Número total de Autores: 1
Tipo de documento: Artigo Científico
Fonte: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 56, n. 1, p. 35-pg., 2025-03-01.
Resumo

We provide a systematic way of calculating the quiver region associated with a given exceptional collection. As an application, we prove that mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-stable sheaves, obtained as the cokernel of morphisms of exceptional mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}-stable bundles, are Bridgeland stable, using the determinant. In the subsequent sections, we focus on the case of even rank 2 instantons over P3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}<^>3$$\end{document} and Q3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_3$$\end{document}, where we prove that instanton sheaves, instanton bundles and perverse instantons are Bridgeland stable and offer a description of the moduli space near its only actual wall. (AU)

Processo FAPESP: 16/25249-0 - Estabilidade de Bridgeland e cruzamento de paredes.
Beneficiário:Victor Do Valle Pretti
Modalidade de apoio: Bolsas no Brasil - Doutorado
Processo FAPESP: 19/05207-9 - Paredes em condições de estabilidade de Bridgeland
Beneficiário:Victor Do Valle Pretti
Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
Processo FAPESP: 22/12883-3 - Regiões Quivers, Instantons sobre variedades Fano
Beneficiário:Victor Do Valle Pretti
Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado