article
Rational curves on smooth hypersurfaces of low degree
published
yes
Timothy D
Browning
author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177
Pankaj
Vishe
author
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.
Mathematical Sciences Publishers2017
eng
Geometric Methods in Algebra and Number Theory
1944-7833
1611.0055310.2140/ant.2017.11.1657
1171657 - 1675
yes
Browning, Timothy D., and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” <i>Geometric Methods in Algebra and Number Theory</i>, vol. 11, no. 7, Mathematical Sciences Publishers, 2017, pp. 1657–75, doi:<a href="https://doi.org/10.2140/ant.2017.11.1657">10.2140/ant.2017.11.1657</a>.
Browning TD, Vishe P. Rational curves on smooth hypersurfaces of low degree. <i>Geometric Methods in Algebra and Number Theory</i>. 2017;11(7):1657-1675. doi:<a href="https://doi.org/10.2140/ant.2017.11.1657">10.2140/ant.2017.11.1657</a>
Browning, Timothy D, and Pankaj Vishe. “Rational Curves on Smooth Hypersurfaces of Low Degree.” <i>Geometric Methods in Algebra and Number Theory</i>. Mathematical Sciences Publishers, 2017. <a href="https://doi.org/10.2140/ant.2017.11.1657">https://doi.org/10.2140/ant.2017.11.1657</a>.
T. D. Browning and P. Vishe, “Rational curves on smooth hypersurfaces of low degree,” <i>Geometric Methods in Algebra and Number Theory</i>, vol. 11, no. 7. Mathematical Sciences Publishers, 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.
T.D. Browning, P. Vishe, Geometric Methods in Algebra and Number Theory 11 (2017) 1657–1675.
Browning, T. D., & Vishe, P. (2017). Rational curves on smooth hypersurfaces of low degree. <i>Geometric Methods in Algebra and Number Theory</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/ant.2017.11.1657">https://doi.org/10.2140/ant.2017.11.1657</a>
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