Instanton bundles on complex projective spaces

• Grant number: 16/11629-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 22, 2016
• End date: August 27, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Marcos Benevenuto Jardim
• Visiting researcher: Giorgio Ottaviani
• Visiting researcher institution: Università degli Studi di Firenze, Italy
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Instanton bundles are a class of algebraic vector bundles, first introduced in mathematical physics as solutions of the Yang-Mills equation over compactified space-time, and later much studied in algebraic geometry. The main questions (irreducibility, smoothness) about the moduli space of instanton bundles on 3-dimensional projective space have been recently settled, but there are many open question regarding instanton bundles on higher dimensional projective spaces. Recently, Davide Vanzo explains that exactly two irreducible components are expected for the moduli space of symplectic instanton bundles on projective spaces of dimension larger than 5. We plan to study the analogous question for the moduli space of all instanton bundles, not necessarily with a symplectic structure. (AU)