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arXiv · 2607.17966

Degenerating Discriminants

Viktoriia Borovik·Clara Briand
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Abstract

We study the behavior of projective dual varieties and discriminants under flat degenerations. For Gr\"obner degenerations, we show that the conormal variety admits a Gr\"obner degeneration with opposite weights on the dual coordinates. Using Whitney stratifications and Sabbah's formula, we describe the irreducible components and multiplicities of the special fiber of this degeneration, and hence of the limiting dual hypersurface. We then extend these results to higher associated hypersurfaces in Grassmannians. As applications, we recover classical formulas for hypersurfaces with isolated singularities, analyze degenerations of generic complete intersections and reciprocal linear spaces, and relate the theory to mixed discriminants of parametrized polynomial systems.

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Viktoriia Borovik, Clara Briand. 2026-07-20. Degenerating Discriminants. https://arxiv.org/abs/2607.17966

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