Rational curves on smooth cubic hypersurfaces over finite fields

Tim Browning; Pankaj Vishe

Rational curves on smooth cubic hypersurfaces over finite fields

Mathematics

Research output: Working paper › Preprint

Abstract

Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.

Original language	English
Number of pages	12
Publication status	Unpublished - 17 Feb 2015

Bibliographical note

12 pages

Keywords

math.AG
math.NT
14H10, 11P55, 14G05

Access to Document

RationCurvesSubmitted manuscript, 156 KB

http://arxiv.org/abs/1502.05028

Programme Grant-New Frameworks in metric Number Theory
Velani, S. & Beresnevich, V.
EPSRC
1/06/12 → 30/11/18
Project: Research project (funded) › Research

Cite this

@techreport{9ee95c52dca74304a21d6c8aeea7b0e6,

title = "Rational curves on smooth cubic hypersurfaces over finite fields",

abstract = "Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.",

keywords = "math.AG, math.NT, 14H10, 11P55, 14G05",

author = "Tim Browning and Pankaj Vishe",

note = "12 pages",

year = "2015",

month = feb,

day = "17",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Rational curves on smooth cubic hypersurfaces over finite fields

AU - Browning, Tim

AU - Vishe, Pankaj

N1 - 12 pages

PY - 2015/2/17

Y1 - 2015/2/17

N2 - Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.

AB - Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.

KW - math.AG

KW - math.NT

KW - 14H10, 11P55, 14G05

M3 - Preprint

BT - Rational curves on smooth cubic hypersurfaces over finite fields

ER -

Rational curves on smooth cubic hypersurfaces over finite fields

Abstract

Bibliographical note

Keywords

Access to Document

Projects

Programme Grant-New Frameworks in metric Number Theory

Cite this