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2017 Rational curves on smooth hypersurfaces of low degree
Timothy Browning, Pankaj Vishe
Algebra Number Theory 11(7): 1657-1675 (2017). DOI: 10.2140/ant.2017.11.1657

Abstract

We establish the dimension and irreducibility of the moduli space of rational curves (of fixed degree) on arbitrary smooth hypersurfaces of sufficiently low degree. A spreading out argument reduces the problem to hypersurfaces defined over finite fields of large cardinality, which can then be tackled using a function field version of the Hardy-Littlewood circle method, in which particular care is taken to ensure uniformity in the size of the underlying finite field.

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Timothy Browning. Pankaj Vishe. "Rational curves on smooth hypersurfaces of low degree." Algebra Number Theory 11 (7) 1657 - 1675, 2017. https://doi.org/10.2140/ant.2017.11.1657

Information

Received: 2 November 2016; Revised: 27 March 2017; Accepted: 23 May 2017; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06775556
MathSciNet: MR3697151
Digital Object Identifier: 10.2140/ant.2017.11.1657

Subjects:
Primary: 14H10
Secondary: 11P55, 14G05

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 7 • 2017
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