Compactifications of conic spaces in del Pezzo 3-fold

Kiryong Chung; Sang-Bum Yoo

doi:10.1016/j.crma.2019.09.003

Algebraic geometry

Compactifications of conic spaces in del Pezzo 3-fold

Presented by: Claire Voisin

Kiryong Chung ¹; Sang-Bum Yoo 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, Volume 357 (2019) no. 9, pp. 729-736.

Abstract
Résumé

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.

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.

Received: 2019-05-23
Accepted: 2019-09-16
Published online: 2019-09-01

DOI: 10.1016/j.crma.2019.09.003

Author's affiliations:

Kiryong Chung ¹; Sang-Bum Yoo 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

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     author = {Kiryong Chung and Sang-Bum Yoo},
     title = {Compactifications of conic spaces in del {Pezzo} 3-fold},
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     pages = {729--736},
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     number = {9},
     year = {2019},
     doi = {10.1016/j.crma.2019.09.003},
     language = {en},
}

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Kiryong Chung; Sang-Bum Yoo. Compactifications of conic spaces in del Pezzo 3-fold. Comptes Rendus. Mathématique, Volume 357 (2019) no. 9, pp. 729-736. doi : 10.1016/j.crma.2019.09.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.09.003/

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