Algebra & Number Theory

Rational curves on smooth hypersurfaces of low degree

Timothy Browning and Pankaj Vishe

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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.

Article information

Source
Algebra Number Theory, Volume 11, Number 7 (2017), 1657-1675.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513096742

Digital Object Identifier
doi:10.2140/ant.2017.11.1657

Mathematical Reviews number (MathSciNet)
MR3697151

Zentralblatt MATH identifier
06775556

Subjects
Primary: 14H10: Families, moduli (algebraic)
Secondary: 11P55: Applications of the Hardy-Littlewood method [See also 11D85] 14G05: Rational points

Keywords
rational curves circle method function fields hypersurfaces

Citation

Browning, Timothy; Vishe, Pankaj. Rational curves on smooth hypersurfaces of low degree. Algebra Number Theory 11 (2017), no. 7, 1657--1675. doi:10.2140/ant.2017.11.1657. https://projecteuclid.org/euclid.ant/1513096742


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