Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 tropical multiplicities and a generalization of the
Sturmfels-Tevelev multiplicity formula in tropical elimination theory to the
case of a nontrivial valuation. For curves, we explore in detail the
relationship between skeletal metrics and lattice lengths on tropicalizations
and show that the maps from the analytification of a curve to the
tropicalizations of its toric embeddings stabilize to an isometry on finite
subgraphs. Other applications include generalizations of Speyer's
well-spacedness condition and the Katz-Markwig-Markwig results on tropical
j-invariants.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph