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.
Original language | English |
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Pages (from-to) | 1657–1675 |
Number of pages | 19 |
Journal | Algebra and Number Theory |
Volume | 11 |
Issue number | 7 |
Early online date | 7 Sept 2017 |
DOIs | |
Publication status | Published - Sept 2017 |
Keywords
- math.AG
- math.NT
- 14H10 (11P55, 14G05)