Rational curves on smooth hypersurfaces of low degree

T.D. Browning, P. Vishe, Geometric Methods in Algebra and Number Theory 11 (2017) 1657–1675.

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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.
Publishing Year
Date Published
2017-09-07
Journal Title
Geometric Methods in Algebra and Number Theory
Acknowledgement
While working on this paper the first author was supported by ERC grant 306457.
Volume
11
Issue
7
Page
1657 - 1675
IST-REx-ID

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Browning TD, Vishe P. Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory. 2017;11(7):1657-1675. doi:10.2140/ant.2017.11.1657
Browning, T. D., & Vishe, P. (2017). Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory, 11(7), 1657–1675. https://doi.org/10.2140/ant.2017.11.1657
Browning, Timothy D, and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” Geometric Methods in Algebra and Number Theory 11, no. 7 (2017): 1657–75. https://doi.org/10.2140/ant.2017.11.1657.
T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7, pp. 1657–1675, 2017.
Browning TD, Vishe P. 2017. Rational curves on smooth hypersurfaces of low degree. Geometric Methods in Algebra and Number Theory. 11(7), 1657–1675.
Browning, Timothy D., and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” Geometric Methods in Algebra and Number Theory, vol. 11, no. 7, Mathematical Sciences Publishers, 2017, pp. 1657–75, doi:10.2140/ant.2017.11.1657.

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