Twisted cubic curves in the Segre variety

Chung, Kiryong; Lee, Wanseok

doi:10.1016/j.crma.2015.09.008

Algebraic geometry

Twisted cubic curves in the Segre variety
[Courbes rationnelles dans la variété de Segre]

Présenté par : Claire Voisin

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

Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1123-1127.

Résumé
Abstract

Soit $X = P^{1} \times P^{1} \times P^{1}$ 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.

Let $X = P^{1} \times P^{1} \times P^{1}$ 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.

Reçu le : 2015-04-30
Accepté le : 2015-09-11
Publié le : 2015-10-23

DOI : 10.1016/j.crma.2015.09.008

Mots clés : Rational curves, Stable maps, Stable sheaves

Affiliations des auteurs :

Chung, Kiryong ¹ ; Lee, Wanseok ²

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Chung, Kiryong; Lee, Wanseok. Twisted cubic curves in the Segre variety. Comptes Rendus. Mathématique, Tome 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/

Bibliographie
Cité par

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