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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1123-1127 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.008
Received : 30 April 2015 ;  accepted : 11 September 2015
Twisted cubic curves in the Segre variety
Courbes rationnelles dans la variété de Segre
 

Kiryong Chung a , Wanseok Lee b,
a Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea 
b Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea 

Corresponding author.
Abstract

Let   be the Segre variety. Let S be the space of twisted cubic curves in X with tri-degree  . In this note, we prove that S is a rational, smooth variety of dimension 6. Also, we compute the Poincaré polynomial of S by stratifying the space into projective space fibration over some base spaces.

The full text of this article is available in PDF format.
Résumé

Soit   la variété de Segre. Soit S l'espace des courbes cubiques rationnelles de tridegré   dans X . Dans cet article, nous prouvons que S est une variété rationnelle, lisse, de dimension 6. Nous calculons également le polynôme de Poincaré de S à l'aide d'une stratification dont les strates sont des fibrés projectifs.

The full text of this article is available in PDF format.

Keywords : Rational curves, Stable maps, Stable sheaves




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