Compactifications of conic spaces in del Pezzo 3-fold

Chung, Kiryong; Yoo, Sang-Bum

doi:10.1016/j.crma.2019.09.003

Algebraic geometry

Compactifications of conic spaces in del Pezzo 3-fold
[Compactifications d'espaces coniques dans la variété de del Pezzo de dimension 3]

Présenté par : Claire Voisin

Chung, Kiryong ¹ ; Yoo, Sang-Bum ²

¹ Department of Mathematics Education, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea
² School of Natural Science, UNIST, 50 UNIST-gil, Ulsan 44919, Republic of Korea

Comptes Rendus. Mathématique, Tome 357 (2019) no. 9, pp. 729-736.

Résumé
Abstract

Soit $V_{5}$ le del Pezzo 3 défini par la section linéaire de dimension 6 de la variété grassmannienne $Gr (2, 5)$ située sous l'enrobage de Plücker. Dans cet article, nous présentons une relation birationnelle explicite de compactifications de courbes rationnelles de degré deux en $V_{5}$ . Au moyen d'un produit, nous obtenons le polynôme de Poincaré virtuel des espaces de modules compactifiés.

Let $V_{5}$ be the del Pezzo 3-fold defined by the 6-dimensional linear section of the Grassmannian variety $Gr (2, 5)$ under the Plücker embedding. In this paper, we present an explicit birational relation of compactifications of degree-two rational curves (i.e. conics) in $V_{5}$ . By a product, we obtain the virtual Poincaré polynomial of compactified moduli spaces.

Reçu le : 2019-05-23
Accepté le : 2019-09-16
Publié le : 2019-09-01

DOI : 10.1016/j.crma.2019.09.003

Affiliations des auteurs :

Chung, Kiryong ¹ ; Yoo, Sang-Bum ²

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     title = {Compactifications of conic spaces in del {Pezzo} 3-fold},
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Chung, Kiryong; Yoo, Sang-Bum. Compactifications of conic spaces in del Pezzo 3-fold. Comptes Rendus. Mathématique, Tome 357 (2019) no. 9, pp. 729-736. doi : 10.1016/j.crma.2019.09.003. http://www.numdam.org/articles/10.1016/j.crma.2019.09.003/

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