Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noether-Lefschetz locus and generalisation of an example due to Mumford   In this article we generalise the well-known example due to Mumford for a
generically non-reduced component of the Hilbert scheme of curves in
$\mathbb{P}^3$ whose general element is smooth. The example considers smooth
curves in smooth cubic surfaces in $\mathbb{P}^3$. In this article we give
similar examples of generically non-reduced component of the Hilbert scheme of
curves in $\mathbb{P}^3$, for every integer $d \ge 5$, whose general element is
a smooth curve contained in a smooth degree $d$ surface in $\mathbb{P}^3$ and
not in any surface of smaller degree. The techniques used are motivated by the
study of Noether-Lefschetz locus.

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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex