Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to lifting tropical curves in surfaces in 3-space   Tropicalization is a procedure that takes subvarieties of an algebraic torus
to balanced weighted rational complexes in space. In this paper, we study the
tropicalizations of curves in surfaces in 3-space. These are balanced rational
weighted graphs in tropical surfaces. Specifically, we study the `lifting'
problem: given a graph in a tropical surface, can one find a corresponding
algebraic curve in a surface? We develop specific combinatorial obstructions to
lifting a graph by reducing the problem to the question of whether or not one
can factor a polynomial with particular support in the characteristic 0 case.
This explains why some unusual tropical curves constructed by Vigeland are not
liftable.

30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org