Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on families of singular curves with hyperelliptic normalizations   We give restrictions on the existence of families of curves on smooth
projective surfaces $S$ of nonnegative Kodaira dimension all having constant
geometric genus $g \geq 2$ and hyperelliptic normalizations. In particular, we
prove a Reider-like result whose proof is ``vector bundle-free'' and relies on
deformation theory and bending-and-breaking of rational curves in $\Sym^2(S)$.
We also give examples of families of such curves.

33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs