Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of primitive pencils for smooth curves   Let $C$ be a smooth curve with gonality $k\ge 6$ and genus $g\ge 2k^2+5k-6$.
We prove that $W^1_d({C})$ has the expected dimension and that the general
element of any irreducible component of $W^1_d({C})$ is primitive if either
$g-k+4\le d\le g-2$ or $d=g-k+3$ and either $k$ is odd or $C$ is not a double
covering of a curve of gonality $k/2$ and genus $k-3$. Even in the latter case
we prove the existence of a complete and primitive $g^1_{g-k+3}$.

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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: q-fin