Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tropical compactification and the Gromov--Witten theory of
  $\mathbb{P}^1$   We use tropical and nonarchimedean geometry to study the moduli space of
genus $0$ stable maps to $\mathbb{P}^1$ relative to two points. This space is
exhibited as a tropical compactification in a toric variety. Moreover, the fan
of this toric variety may be interpreted as a moduli space for tropical
relative stable maps with the same discrete data. As a consequence, we confirm
an expectation of Bertram and the first two authors, that the tropical Hurwitz
cycles are tropicalizations of classical Hurwitz cycles. As a second
application, we obtain a full descendant correspondence for genus $0$ relative
invariants of $\mathbb{P}^1$.

23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas