Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brill-Noether general K3 surfaces with the maximal number of elliptic
  pencils of minimal degree   We explicitly construct Brill--Noether general $K3$ surfaces of genus $4,6$
and $8$ having the maximal number of elliptic pencils of degrees $3, 4$ and
$5$, respectively, and study their moduli spaces and moduli maps to the moduli
space of curves. As an application we prove the existence of Brill--Noether
general $K3$ surfaces of genus $4$ and $6$ without stable Lazarsfeld--Mukai
bundles of minimal $c_2$.

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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc