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RATIONAL CURVES ON CUBIC HYPERSURFACES OVER FINITE FIELDS
Author(s) -
Mânzăţeanu Adelina
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12073
Subject(s) - mathematics , hypersurface , irreducibility , function field , finite field , moduli space , dimension (graph theory) , rational function , degree (music) , mathematical analysis , pure mathematics , field (mathematics) , cubic surface , moduli , combinatorics , physics , quantum mechanics , acoustics
Given a smooth cubic hypersurface X over a finite field of characteristic greater than 3 and two generic points on X , we use a function field analogue of the Hardy–Littlewood circle method to obtain an asymptotic formula for the number of degree d k ‐rational curves on X passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough d .
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