Title	Bounding the Betti numbers of real tropical varieties.
Creator	Renaudineau, Arthur
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-09-09T09:26
Description	Real tropical varieties are polyhedral objects which are in some cases isotopic to real algebraic varieties. We will introduce those objects and show an upper bound on their Betti numbers. These bounds are given in terms of the dimension of tropical homology groups modulo 2 of the underlying tropical variety, and are derived from a certain spectral sequence. In the case of hypersurfaces, we prove that tropical homology groups are torsion free, implying a bound conjectured by Itenberg on the Betti numbers of the real part of a real hypersurface near the tropical limit in terms of Hodge numbers of the complexification. This is a joint work with Kristin Shaw, and with Charles Arnal and Kristin Shaw.
Extent	45.0 minutes
Subject	Mathematics; Algebraic geometry; Combinatorics
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Université de Lille
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2020-03-08
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0389501
URI	http://hdl.handle.net/2429/73693
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Bounding the Betti numbers of real tropical varieties. Renaudineau, Arthur

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