On generalized Wrońskians

Abstract

The Wroński determinant (Wrońskian), usually introduced in standard courses in Ordinary Differential Equations (ODE), is a very useful tool in algebraic geometry to detect ramification loci of linear systems. The present survey aims to describe some “materializations” of the Wrońskian and of its close relatives, the generalized Wrońskians, in algebraic geometry. Emphasis will be put on the relationships between Schubert Calculus and ODE.