Some contributions of Edoardo Ballico to Moduli spaces and their applications

Abstract

This is a contribution to the Special Volume in Celebration of the 70th Birthday of Edoardo Ballico. First, I describe how some results of Ballico on moduli of vector bundles and categories coherent sheaves were useful for solving problems in a variety of areas: Homological Mirror Symmetry, symplectic geometry, Hodge theory, mathematical physics, noncommutative geometry. Second, I summarise some strong results of Ballico about the number of components of moduli scheme of sheaves and about the existence of singularities on moduli of vector bundles. Third, the text includes a section written by Wojciech Kucharz, about the work of Ballico on moduli flexibility of real manifolds.