Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polar degree of hypersurfaces with 1-dimensional singularities   We prove a formula for the polar degree of projective hypersurfaces in terms
of the Milnor data of the singularities, extending to 1-dimensional
singularities the Dimca-Papadima result for isolated singularities. We discuss
the semi-continuity of the polar degree in deformations, and we classify the
homaloidal cubic surfaces with 1-dimensional singular locus. Some open
questions are pointed out along the way.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex