Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the complexity group of stable curves   In this paper, we study combinatorial properties of stable curves. To the
dual graph of any nodal curve, it is naturally associated a group, which is the
group of components of the N\'eron model of the generalized Jacobian of the
curve. We study the order of this group, called the complexity. In particular,
we provide a partial characterization of the stable curves having maximal
complexity, and we provide an upper bound, depending only on the genus $g$ of
the curve, on the maximal complexity of stable curves; this bound is
asymptotically sharp for $g\gg 0$. Eventually, we state some conjectures on the
behavior of stable curves with maximal complexity, and prove partial results in
this direction.

21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg