Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geography of Brill-Noether loci for small slopes   Let $X$ be a non-singular projective curve of genus $g\ge2$ over an
algebraically closed field of characteristic zero. Let $\mo$ denote the moduli
space of stable bundles of rank $n$ and degree $d$ on $X$ and $\wn $ the
Brill-Noether loci in $\mo .$ We prove that, if $0\leq d \leq n $ and $\wn $ is
non-empty, then it is irreducible of the expected dimension and smooth outside
$\wnn$. We prove further that in this range $\wn$ is non-empty if and only if
$d>0$, $n\leq d+(n-k)g$ and $(n,d,k) \not= (n,n,n)$. We also prove
irreducibility and non-emptiness for the semistable Brill-Noether loci.

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The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg