Geodesic
On the Hyperplane Sections Through two Given Points of an Algebraic Variety
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 128-133

Voir la notice de l'article provenant de la source Cambridge University Press

1. Let k be an infinite field and let V/k be an irreducible variety of dimension ≧ 2 in a projective n-space Pn over k. Let P and Q be two k-rational points on V In this paper, we describe ideal-theoretically the generic hyperplane section of V through P and Q (Theorem 1) and prove that the section is almost always an absolutely irreducible variety over k 1/pe if V/k is absolutely irreducible (Theorem 3). As an application (Theorem 4), we give a new simple proof of an important special case of the existence of a curve connecting two rational points of an absolutely irreducible variety [4], namely any two k-rational points on V/k can be connected by an irreducible curve.I wish to thank Professor A. Seidenberg for his continued advice and encouragement on my thesis research. 
Kuan, Wei-Eihn. On the Hyperplane Sections Through two Given Points of an Algebraic Variety. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 128-133. doi: 10.4153/CJM-1970-016-x
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