Geometry of cubic and quartic hypersurfaces over finite fields

被引：0

作者：

Ballico, E ^{[1
]}

机构：

[1] Univ Trent, Dept Math, I-38050 Povo, TN, Italy

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2002年 / 8卷 / 04期

关键词：

cubic hypersurface; quartic hypersurface; cubic hypersurface defined over GF(q); Finite Field Nullstellensatz; polar curve; linear subspace; cubic surface; finite projective space;

D O I：

10.1006/ffta.2002.0364

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Y subset of P-n be a cubic hypersurface defined over GF(q). Here, we study the Finite Field Nullstellensatz of order [q/3] for the set Y(q) of its GF(q)-points, the existence of linear subspaces of PG(n, q) contained in Y(q) and the possibility to join any two points of Y(q) by the union of two lines of PG(n, q) entirely contained in Y(q). We also study the existence of linear subspaces defined over GF(q) for the intersection of Y with s quadrics and for quartic hypersurfaces. (C) 2002 Elsevier Science (USA).

引用

页码：554 / 569

页数：16

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