UNIRATIONALITY OF CUBIC HYPERSURFACES

By J. Kollár. Journal of the Institute of Mathematics of Jussieu, 2000

92 citations recorded by the source corpus.

Segre proved that a smooth cubic surface over $Q$ is unirational if and only if it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields. AMS 2000 Mathematics subject classification: Primary 14G05; 14G15. Secondary 11G25; 11D25

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e1cb2409af133c26efeebe8f008dd248bc504e32

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In Applied Mathematics

1. Keiji Oguiso
2. Zinovy Reichstein
3. Tuyen T. T. Truong
4. Alexander Duncan

In Geometry and Topology

1. Tuyen T. T. Truong
2. Keiji Oguiso
3. Zinovy Reichstein
4. Alexander Duncan
5. Alexander S. Merkurjev
6. D. Huybrechts
7. E. Markman
8. Nguyen-Bac Dang

Citations in the corpus

• Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy (2013, background): “is not rational ([IM71], [CG72], [AM72], [Ko95], [Be12]). However, in dimension ≥ 3, there is essentially no general method to conclude M is rational or unirational, and this is in general very hard ([Ko02], see also the excellent survey [Ko01]). For instance, the following Question 1.4, which is cl”
• Versality of algebraic group actions and rational points on twisted varieties (2011, background): “([Kol02]) Let X ⊂ Pk be a smooth cubic hypersurface where n ≥ 3.”