On the Thom-Boardman Symbols for Polynomial Multiplication Maps

Details On the Thom-Boardman Symbols for Polynomial Multiplication Maps On the Thom-Boardman Symbols for Polynomial Multiplication Maps

2009-02-09

arxiv.org/abs/0902.1518v1

Mathematics

Commutative Algebra

First draft, comments are welcome

Scientific paper

The Thom-Boardman symbol was first introduced by Thom in 1956 to classify singularities of differentiable maps. It was later generalized by Boardman to a more general setting. Although the Thom-Boardman symbol is realized by a sequence of non-increasing, nonnegative integers, to compute those numbers is, in general, extremely difficult. In the case of polynomial multiplication maps, Robert Varley conjectured that computing the Thom-Boardman symbol for polynomial multiplication reduces to computing the successive quotients and remainders for the Euclidean algorithm applied to the degrees of the two polynomials. In this paper, we confirm this conjecture.

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