Free rational curves on low degree hypersurfaces and the circle method
Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748.
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Author
Browning, Timothy DISTA 
;
Sawin, Will
;
Sawin, WillCorresponding author has ISTA affiliation
Department
Abstract
We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle.
Publishing Year
Date Published
2023-04-12
Journal Title
Algebra and Number Theory
Publisher
Mathematical Sciences Publishers
Acknowledgement
The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.
Volume
17
Issue
3
Page
719-748
ISSN
eISSN
IST-REx-ID
Cite this
Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719
Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719
Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/ant.2023.17.719.
T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” Algebra and Number Theory, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023.
Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748.
Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:10.2140/ant.2023.17.719.
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