Moduli spaces of Steiner bundles on the projective plane

• Grant number: 14/11169-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: November 05, 2014
• End date: December 04, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Jean Vallès
• Visiting researcher institution: Université de Pau et des Pays de l'Adour, France
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The goal of this project is to give a new classification of a particular family of stable vector bundles E on the projective plane, which are called Steiner bundles. In order to do so, we propose to stratify the moduli space of stable vector bundles on the projective plane, of rank two and fixed Chern classes, using the so-called ramification degree. The ramification degree is defined as the lowest integer such that the twist of the second symmetric power of E by this integer admits global sections. The importance of the ramification degree is given by the strong relationship between the stability of the bundle E and the global sections of its symmetric power. Indeed, we know that if E is stable then h^0((S^2E)(-c_1(E)))=0. We choose to focus on Steiner bundle because they are dense in the considered moduli space. (AU)