With Wronskian through the Looking Glass

Abstract

In the work of Mukhin and Varchenko from 2002, a Wronskian map was introduced from the variety of full flags in a finite-dimensional vector space into a product of projective spaces. We establish a precise relationship between this map and the Plücker map. This allows us to recover the result of Varchenko and Wright, saying that the polynomials appearing in the image of the Wronsky map are the initial values of the tau-functions for the Kadomtsev-Petviashvili hierarchy.