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Singular Tropical Hypersurfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 29 Jun 2011Embargo end date: 01 Jan 2010 Spain, Argentina Publisher:Springer Science and Business Media LLCJournal:Discrete & Computational Geometry, volume 47, pages 430-453 (issn: 0179-5376, eissn: 1432-0444,

Authors: Dickenstein, Alicia; Tabera Alonso, Luis Felipe;

doi: 10.1007/s00454-011-9364-6 , 10.48550/arxiv.1012.5812

arXiv: http://arxiv.org/abs/1012.5812

handle: 10902/5253 , 11336/19893

Singular Tropical Hypersurfaces

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Abstract

We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves.

Several improvements. Added a discussion in section 4 on the relationship of our results and previous results on tropical discriminants

Countries

Spain, Argentina

Related Organizations

University of Cantabria
Spain
National Scientific and Technical Research Council
Argentina
University of Buenos Aires
Argentina

Keywords

Singularity, Euler Derivative, Mathematics - Algebraic Geometry, Tropical geometry, Tropical Geometry, Euler derivative, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Mathematics - Combinatorics, Combinatorics (math.CO), https://purl.org/becyt/ford/1, Algebraic Geometry (math.AG), Discriminant

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	11
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average