Unirationality and geometric unirationality for hypersurfaces in positive characteristics

2020/02/21 by Oguiso, Keiji, Schröer, Stefan
#14G05 #14G17 #14J26 #14J70 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.09228

Abstract

Building on work of Segre and Koll'ar on cubic hypersurfaces, we construct over imperfect fields of characteristic p≥ 3 particular hypersurfaces of degree p, which show that geometrically rational schemes that are regular and whose rational points are Zariski dense are not necessarily unirational. A likewise behaviour holds for certain cubic surfaces in characteristic p=2.

Related

• Unirationality of cubic hypersurfaces
• A transfer principle for unirationality
• Unirationality of varieties described by families of projective hypersurfaces
• Unirationality of RDP Del Pezzo surfaces of degree 2
• Unirationality of hypersurfaces via highly tangent lines