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 …
[PDF][PDF] Nonarchimedean geometry, tropicalization, and metrics on curves
We develop a number of general techniques for comparing analytifications and
tropicalizations of algebraic varieties. Our basic results include a projection formula for …
tropicalizations of algebraic varieties. Our basic results include a projection formula for …
Nonarchimedean geometry, tropicalization, and metrics on curves
We develop a number of general techniques for comparing analytifications and
tropicalizations of algebraic varieties. Our basic results include a projection formula for …
tropicalizations of algebraic varieties. Our basic results include a projection formula for …
A field of generalised Puiseux series for tropical geometry
T Markwig - arXiv preprint arXiv:0709.3784, 2007 - arxiv.org
In this paper we define a field K of characteristic zero with valuation whose value group is
the real numbers, and we show that this field of generalised Puiseux series is algebraically …
the real numbers, and we show that this field of generalised Puiseux series is algebraically …
Bitangents of tropical plane quartic curves
We study smooth tropical plane quartic curves and show that they satisfy certain properties
analogous to (but also different from) smooth plane quartics in algebraic geometry. For …
analogous to (but also different from) smooth plane quartics in algebraic geometry. For …
From curves to tropical Jacobians and back
For a curve over an algebraically closed field that is complete with respect to a nontrivial
valuation, we study its tropical Jacobian. We first tropicalize the curve and then use the …
valuation, we study its tropical Jacobian. We first tropicalize the curve and then use the …
Smooth tropical surfaces with infinitely many tropical lines
MD Vigeland - Arkiv för Matematik, 2010 - Springer
We study the tropical lines contained in smooth tropical surfaces in ℝ 3. On smooth tropical
quadric surfaces we find two one-dimensional families of tropical lines, like in classical …
quadric surfaces we find two one-dimensional families of tropical lines, like in classical …
Constructing smooth and fully faithful tropicalizations for Mumford curves
P Jell - Selecta Mathematica, 2020 - Springer
The tropicalization of an algebraic variety X is a combinatorial shadow of X, which is
sensitive to a closed embedding of X into a toric variety. Given a good embedding, the …
sensitive to a closed embedding of X into a toric variety. Given a good embedding, the …
How to repair tropicalizations of plane curves using modifications
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The
purpose of this article is to advertise tropical modifications as a tool to locally repair bad …
purpose of this article is to advertise tropical modifications as a tool to locally repair bad …
Introduction to tropical algebraic geometry
D Maclagan - Tropical geometry and integrable systems, 2012 - books.google.com
This is an expository introduction to tropical algebraic geometry based on my lectures at the
Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4–8, 2011, and at …
Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4–8, 2011, and at …