Logarithmic limit sets of real semi-algebraic sets

By D. Alessandrini. 2007

62 citations recorded by the source corpus.

This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the logarithmic limit sets of complex algebraic sets hold in the real case. This include the polyhedral structure and the relation with the theory of non-archimedean fields, tropical geometry and Maslov dequantization.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e72052abb5be34d91a36b96d73aea1c8c9b1ae38

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In Computational Theory and Mathematics

1. Claus Scheiderer
2. Josephine Yu
3. Philipp Jell
4. Martyn Marshall
5. Jiawang Nie
6. K. Schmuedgen
7. Salma Kuhlmann

In Geometry and Topology

1. Claus Scheiderer
2. Josephine Yu
3. Philipp Jell
4. Martyn Marshall
5. Jiawang Nie
6. K. Schmuedgen

Citations in the corpus

• Real Tropicalization and Analytification of Semialgebraic Sets (2018, methodology): “f RT2 dened by X3 Y X2 Y2 1 0: The real tropicalization of f(x;y) 2K2 : x3 + 2y x2 y2 1 0g consists of the shaded region and the point (0;1), but not the two red segments. Compare with Figure 7 in [Ale13]. Figure 1. Real tropicalizations of sets and polynomial inequalities. if a point a2Knsatises f0”