Effective Results on p-adic Tropical Discriminants

Details Effective Results on p-adic Tropical Discriminants Effective Results on p-adic Tropical Discriminants

2012-01-30

arxiv.org/abs/1201.6401v2

Mathematics

Algebraic Geometry

12 pages

Scientific paper

We study A-discriminants from a p-adic point of view, refining earlier work on the tropical discriminant. In particular, we study the case where A is a collection of n+3 points in Z^n in general position, and give an algorithm to compute the image of the A-discriminant variety under the p-adic valuation map. Consequences of our approach include tight lower and upper bounds, of order quadratic in n, for the number of connected components of the complement of the amoeba closure. We also detail a Sage package for plotting certain p-adic discriminant amoebae, and present explicit examples of point sets yielding discriminant amoebae with extremal behavior. We also discuss the setting where A has arbitrary cardinality.

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