Weierstrass Points Methods for Schubert Calculus

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Abstract Let F be a complete flag of a complex n-dimensional vectorspace V. It will be shown that a k-plane in special position with respect to the given flag is the formal analogous of a Weierstrass point on a curve. In fact, the k-planes in special position with respect to the flag F form the zero locus of a section of the top exterior power of the dual of the tautological bundle, which we named Schubert wronskian. As special Weierstrass points may be detected as zeros of the wronskian and some of its derivatives, the same holds for k-planes in more special position, being zeros of the Schubert wronskian and some derivatives. The Schubert index corresponds to the Weierstrass gap sequence at a point. The complete analogy between Weierstrass points theory and Schubert calculus via wronskians leads to a simple (re)formulation of the latter in terms of rings of differential operators of the kth exterior power of V. In particular Pieri's formula translates into Leibniz's rule and Giambelli's formula into integration by parts.

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