Phase limit sets of linear spaces and discriminants

Mounir Nisse; Frank Sottile

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arXiv · 2411.19018

Phase limit sets of linear spaces and discriminants

Mounir Nisse·Frank Sottile

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Abstract

We show that the closure of the coamoeba of a linear space/hyperplane complement is the union of products of coamoebas of hyperplane complements coming from flags of flats, and relate this to the Bergman fan. Using the Horn-Kapranov parameterization of a reduced discriminant, this gives a partial description of the phase limit sets of discriminants and duals of toric varieties. When d=3, we show that each 3-dimensional component of the phase limit set of the discriminant is a prism over a discriminant coamoeba in dimension 2, which has a polyhedral description by a result of Nilsson and Passare.

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Mounir Nisse, Frank Sottile. 2024-11-28. Phase limit sets of linear spaces and discriminants. https://arxiv.org/abs/2411.19018

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