Geometria dos espaços de moduli de feixes sem torção em espaços projetivos

Author(s)

Charles Aparecido de Almeida

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2019-01-25

Examining board members

Marcos Benevenuto Jardim; Abdelmoubine Amar Henni; Renato Vidal da Silva Martins; Danilo Dias da Silva; Kostiantyn Iusenko

• Advisor: Marcos Benevenuto Jardim

Abstract

Our goal is to study the geometry of moduli spaces of rank 2 sheaves on projective spaces. We present a new family of monads whose cohomology is a stable rank two vector bundle on $\PP$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. Such facts are used to prove that the moduli space of stable rank two vector bundles of zero first Chern class and second Chern class equal to 5 has exactly three irreducible components. Additionally, we describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the tridimensional projective space whose generic point corresponds to non-locally free sheaves. As applications, we prove that the number of such components grows as the second Chern class grows. Additionally, we proved that $\mathcal{M}(-1,2,4)$ is irreducible; $\mathcal{M}(-1,2,2)$ has at least two irreducible components, such that the intersection is non-empty and that $\mathcal{M}(-1,2,0)$ has at least four irreducible components, and that at least three of them has non-empty intersection (AU)

• FAPESP's process: 14/08306-4 - Vector bundles over projective spaces
• Grantee: Charles Aparecido de Almeida
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)