Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of
  Picard number 2   Let $g$ and $c$ be any integers satisfying $g\geq3$ and $0\leq c\leq
\lfloor\frac{g-1}{2}\rfloor$. It is known that there exists a polarized K3
surface $(X,H)$ such that $X$ is a K3 surface of Picard number 2, and $H$ is a
very ample line bundle on $X$ of sectional genus $g$ and Clifford index $c$, by
Johnsen and Knutsen([J-K] and [Kn]). In this paper, we give a necessary and
sufficient condition for a Lazarsfeld-Mukai bundles of rank 2 associated with a
smooth curve $C$ belonging to the linear system $|H|$ and a base point free
pencil on $C$ not to be $H$-slope stable.

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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: econ