[图书][B] Introduction to tropical geometry
D Maclagan, B Sturmfels - 2021 - books.google.com
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral
tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the …
tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the …
Tropical mathematics
D Speyer, B Sturmfels - Mathematics Magazine, 2009 - Taylor & Francis
This article is based on the Clay Mathematics Senior Scholar Lecture that was delivered by
Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture was the tropical …
Bernd Sturmfels in Park City, Utah, on July 22, 2004. The topic of this lecture was the tropical …
Analytification is the limit of all tropicalizations
S Payne - arXiv preprint arXiv:0805.1916, 2008 - arxiv.org
arXiv:0805.1916v3 [math.AG] 11 Mar 2009 Page 1 arXiv:0805.1916v3 [math.AG] 11 Mar 2009
ANALYTIFICATION IS THE LIMIT OF ALL TROPICALIZATIONS SAM PAYNE Abstract. We …
ANALYTIFICATION IS THE LIMIT OF ALL TROPICALIZATIONS SAM PAYNE Abstract. We …
Tropical algebraic geometry
A Gathmann - arXiv preprint math/0601322, 2006 - arxiv.org
Tropical algebraic geometry is an active new field of mathematics that establishes and
studies some very general principles to translate algebro-geometric problems into purely …
studies some very general principles to translate algebro-geometric problems into purely …
Tropical discriminants
A Dickenstein, E Feichtner, B Sturmfels - Journal of the American …, 2007 - ams.org
Tropical geometry is used to develop a new approach to the theory of discriminants and
resultants in the sense of Gel $'$ fand, Kapranov and Zelevinsky. The tropical $ A …
resultants in the sense of Gel $'$ fand, Kapranov and Zelevinsky. The tropical $ A …
Tropical fans and the moduli spaces of tropical curves
A Gathmann, M Kerber, H Markwig - Compositio Mathematica, 2009 - cambridge.org
We give a rigorous definition of tropical fans (the 'local building blocks for tropical varieties')
and their morphisms. For a morphism of tropical fans of the same dimension we show that …
and their morphisms. For a morphism of tropical fans of the same dimension we show that …
Elimination theory for tropical varieties
B Sturmfels, J Tevelev - arXiv preprint arXiv:0704.3471, 2007 - arxiv.org
arXiv:0704.3471v1 [math.AG] 26 Apr 2007 Page 1 arXiv:0704.3471v1 [math.AG] 26 Apr 2007
ELIMINATION THEORY FOR TROPICAL VARIETIES BERND STURMFELS AND JENIA …
ELIMINATION THEORY FOR TROPICAL VARIETIES BERND STURMFELS AND JENIA …
How to draw tropical planes
S Herrmann, A Jensen, M Joswig… - arXiv preprint arXiv …, 2008 - arxiv.org
The tropical Grassmannian parameterizes tropicalizations of linear spaces, while the
Dressian parameterizes all planes in $\TP^{n-1} $. We study these parameter spaces and …
Dressian parameterizes all planes in $\TP^{n-1} $. We study these parameter spaces and …
Lifting tropical intersections
B Osserman, S Payne - Documenta Mathematica, 2013 - ems.press
We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to
algebraic intersection points with expected multiplicities, provided that the tropicalizations …
algebraic intersection points with expected multiplicities, provided that the tropicalizations …
Geometry of the restricted Boltzmann machine
The restricted Boltzmann machine is a graphical model for binary random variables. Based
on a complete bipartite graph separating hidden and observed variables, it is the binary …
on a complete bipartite graph separating hidden and observed variables, it is the binary …