Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 7 (2017), 1657-1675.
Rational curves on smooth hypersurfaces of low degree
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.
Algebra Number Theory, Volume 11, Number 7 (2017), 1657-1675.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H10: Families, moduli (algebraic)
Secondary: 11P55: Applications of the Hardy-Littlewood method [See also 11D85] 14G05: Rational points
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