The number of reducible space curves over a finite field

被引：4

作者：

Cesaratto, Eda ^{[1
,2
]}

Gathen, Joachim von Zur ^{[3
]}

Matera, Guillermo ^{[1
,2
]}

机构：

[1] Univ Nacl Gen Sarmiento, Inst Desarrollo Humano, Buenos Aires, DF, Argentina

[2] Natl Council Sci & Technol CONICET, Buenos Aires, DF, Argentina

[3] Univ Bonn, B IT, D-53113 Bonn, Germany

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 04期

关键词：

Finite fields; Rational points; Algebraic curves; Asymptotic behavior; Chow variety; Irreducibility; Absolute irreducibility; POLYNOMIALS; VARIETIES; POINTS;

D O I：

10.1016/j.jnt.2012.08.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by the appropriate Chow variety, and provides bounds on the probability that a random curve over a finite field is reducible. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1409 / 1434

页数：26

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