Invariants of pencils of binary quintics
Dr. Matthias Meulien
Chennai Mathematical Institute.
05-12-03 (Institute Colloquium)

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Abstract

Our goal is to describe the invariants of the natural action of SL2 on the homogenous coordinate ring of the Grassmannian of pencils of binary quintics.

To succeed, we first extend T. Springer's formula (for the Poincare series of the invariant algebra of a binary quantic) to the homogeneous coordinate ring of a Grassmannian. The following point consists in the identification of a homogeneous system of parameters. It is possible thanks to the Wronskian morphism which leads to a characterization of the stability on the Grassmannian. Then the order 4 and degree 2 covariants must be studied which provides a few geometric statements. Our techniques also allow to describe the invariant algebras of pencils of cubics and quartics. What's more the Wronskian study leads to new plethysm formulas.

The talk is intended for a general audience, and we will only give an outline of the previous ideas.