Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry on nodal curves   Given a family $X/B$ of nodal curves, we construct canonically and compatibly
with base-change, via an explicit blow-up of the Cartesian product $X^r/B$, a
family $W^r(X/B)$ parametrizing length-$r$ subschemes of fibres of $X/B$ (plus
some additional data). Though $W^r(X/B)$ is singular, the important sheaves on
it are locally free, which allows us to study intersection theory on it and
deduce enumerative applications, including some relative multiple point
formulae, enumerating the length-$r$ schemes contained simultaneously in some
fibre of $X/B$ and some fibre of a given map from $X$ to a smooth variety.

7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph