Wave fronts and (almost) free divisors
Susumu Tanabe
TL;DR
This paper describes how wave fronts from algebraic hypersurfaces relate to discriminantal loci of tame polynomials, providing examples where these wave fronts form free or almost free divisors near focal points.
Contribution
It introduces a method to describe wave fronts using pull-backs of discriminantal loci and demonstrates examples of free/almost free divisors arising in this context.
Findings
Wave fronts can be described via pull-backs of discriminantal loci.
Examples of wave fronts forming free or almost free divisors are provided.
The approach links algebraic hypersurfaces with divisor theory near focal points.
Abstract
In this note we present a description of wave front evolving from an algebraic hypersurface by means of a pull-back of the discriminantal loci of a tame polynomial via a polynomial mapping. As an application we give examples of wave fronts which define free/almost free divisors near the focal point.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Advanced Algebra and Geometry