Complex surfaces of general type with K2 = 3,4 and pg = q = 0

Park, Heesang; Shin, Dongsoo; Yang, Yoonjeong

doi:10.1016/j.crma.2019.02.006

Algebraic geometry

Complex surfaces of general type with K² = 3,4 and p_g = q = 0
[Surfaces complexes de type général avec K² = 3,4 et p_g = q = 0]

Présenté par : Claire Voisin

Park, Heesang ¹ ; Shin, Dongsoo ² ; Yang, Yoonjeong ²

¹ Department of Mathematics, Konkuk University, Seoul 05029, Republic of Korea
² Department of Mathematics, Chungnam National University, Daejeon 34134, Republic of Korea

Comptes Rendus. Mathématique, Tome 357 (2019) no. 3, pp. 291-295.

Résumé
Abstract

Nous construisons des surfaces complexes de type général avec $p_{g} = 0$ et $K^{2} = 3, 4$ (appelées surfaces de Keum–Naie), comme revêtements doubles de surfaces d'Enriques. Notre construction diffère de celle utilisée originellement par Keum–Naie. Comme application, nous montrons qu'il existe une $(- 4)$ -courbe sur une telle surface avec $K^{2} = 3$ , ce qui suggère l'existence d'une relation particulière entre les surfaces de Keum–Naie satisfaisant $K^{2} = 3$ et $K^{2} = 4$ .

We construct complex surfaces of general type with $p_{g} = 0$ and $K^{2} = 3, 4$ as double covers of Enriques surfaces (called Keum–Naie surfaces) with a different way to the original constructions of Keum and Naie. As a result, we show that there is a $(- 4)$ -curve on the example with $K^{2} = 3$ , which might imply a special relation between Keum–Naie surfaces with $K^{2} = 3$ and $K^{2} = 4$ .

Reçu le : 2018-11-18
Accepté le : 2019-02-28
Publié le : 2019-03-01

DOI : 10.1016/j.crma.2019.02.006

Affiliations des auteurs :

Park, Heesang ¹ ; Shin, Dongsoo ² ; Yang, Yoonjeong ²

¹ Department of Mathematics, Konkuk University, Seoul 05029, Republic of Korea
² Department of Mathematics, Chungnam National University, Daejeon 34134, Republic of Korea

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     author = {Park, Heesang and Shin, Dongsoo and Yang, Yoonjeong},
     title = {Complex surfaces of general type with {\protect\emph{K}\protect\textsuperscript{2} = 3,4} and \protect\emph{p}\protect\textsubscript{\protect\emph{g}} = \protect\emph{q} = 0},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {291--295},
     publisher = {Elsevier},
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     year = {2019},
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}

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Park, Heesang; Shin, Dongsoo; Yang, Yoonjeong. Complex surfaces of general type with K² = 3,4 and p_g = q = 0. Comptes Rendus. Mathématique, Tome 357 (2019) no. 3, pp. 291-295. doi : 10.1016/j.crma.2019.02.006. http://www.numdam.org/articles/10.1016/j.crma.2019.02.006/

Bibliographie
Cité par

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[5] Naie, D. Surfaces d'Enriques et une construction de surfaces de type général avec $p_{g} = 0$ , Math. Z., Volume 215 (1994), pp. 269-280

[6] Rito, C. Some bidouble planes with $p_{g} = q = 0$ and $4 \leq K^{2} \leq 7$ , Int. J. Math., Volume 26 (2015) no. 5

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