Geometry of Cubic and Quartic Hypersurfaces over Finite Fields

✍ Scribed by E. Ballico

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 188 KB
• Volume: 8
• Category: Article
• ISSN: 1071-5797
• DOI: 10.1006/ffta.2002.0364

✦ Synopsis

Let Y & P n be a cubic hypersurface defined over GFðqÞ. Here, we study the Finite Field Nullstellensatz of order ½q=3 for the set Y ðqÞ of its GFðqÞ-points, the existence of linear subspaces of PGðn; qÞ contained in Y ðqÞ and the possibility to join any two points of Y ðqÞ by the union of two lines of PGðn; qÞ entirely contained in Y ðqÞ. We also study the existence of linear subspaces defined over GFðqÞ for the intersection of Y with s quadrics and for quartic hypersurfaces.