Free rational curves on low degree hypersurfaces and the circle method
Algebraic Geometry
2023-04-26 v2 Number Theory
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.
Keywords
Cite
@article{arxiv.1810.06882,
title = {Free rational curves on low degree hypersurfaces and the circle method},
author = {Tim Browning and Will Sawin},
journal= {arXiv preprint arXiv:1810.06882},
year = {2023}
}
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34 pages