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Oberseminar WiSe 2009/10 Zusammenfassung des Vortrags von B. Hovinen

The Open Swallowtail as a Matrix-Factorisation

The (generalised) open swallowtail, as studied by Arnol'd and Givental, is a stratum of univariate polynomials with certain root-multiplicities. Its coordinate-ring can be viewed as a module over the classical discriminant of polynomials of appropriate degree. In this talk, I will describe the open swallowtail from this algebraic perspective and show how, in principle, to construct its presentation-matrix explicitly. I will then give some simple applications of this construction to the root-structure of polynomials.