Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Even Sets of Lines on Quartic Surfaces   An effective divisor D on a smooth (compact complex) surface X is called
even, if its class $[D] \in H^2(X,\Z)$ is divisible by 2. D may be assumed
reduced w.l.o.g. Then D being even is equivalent to the existence of a double
cover $Y \to X$ branched exactly over D.
  The aim of this note is to study arrangements of $n \leq 10$ distinct lines
on a smooth quartic surface $X \subset \P_3$, which form an even divisor in
this sense. The result is that for $n \leq 8$ there are no unexpected ones (one
type of six lines, four types of eight lines). And for n=10 a partial
classification is given in the following sense: Each even set of ten lines on a
smooth quartic surface is of one of eleven different types. At the moment I do
not know which of these types do actually occur. The proof for these facts is
messy, essentially checking cases.

10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex