Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The gonality theorem of Noether for hypersurfaces   It is well known since Noether that the gonality of a smooth plane curve of
degree d>3 is d-1. Given a k-dimensional complex projective variety X, the most
natural extension of gonality is probably the degree of irrationality, that is
the minimum degree of a dominant rational map from X to $\mathbb{P}^k$. In this
paper we are aimed at extending the assertion on plane curves to smooth
hypersurfaces in $\mathbb{P}^n$ in terms of degree of irrationality. We prove
that both surfaces in $\mathbb{P}^3$ and threefolds in $\mathbb{P}^4$ of
sufficiently large degree d have degree of irrationality d-1, except for
finitely many cases we classify, whose degree of irrationality is d-2. To this
aim we use Mumford's technique of induced differentials and we shift the
problem to study first order congruences of lines of $\mathbb{P}^n$. In
particular, we also slightly improve the description of such congruences in
$\mathbb{P}^4$ and we provide a bound on degree of irrationality of
hypersurfaces of arbitrary dimension.

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th