Algebraic geometry
Twisted cubic curves in the Segre variety
Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1123-1127.

Let X=P1×P1×P1 be the Segre variety. Let S be the space of twisted cubic curves in X with tri-degree (1,1,1). 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.

Soit X=P1×P1×P1 la variété de Segre. Soit S l'espace des courbes cubiques rationnelles de tridegré (1,1,1) 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.008
Keywords: Rational curves, Stable maps, Stable sheaves
Chung, Kiryong 1; Lee, Wanseok 2

1 Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
2 Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
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Chung, Kiryong; Lee, Wanseok. Twisted cubic curves in the Segre variety. Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1123-1127. doi : 10.1016/j.crma.2015.09.008. http://www.numdam.org/articles/10.1016/j.crma.2015.09.008/

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