Algebraic geometry
Complex surfaces of general type with K2 = 3,4 and pg = q = 0
Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 291-295.

We construct complex surfaces of general type with $pg=0$ and $K2=3,4$ 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 $K2=3$, which might imply a special relation between Keum–Naie surfaces with $K2=3$ and $K2=4$.

Nous construisons des surfaces complexes de type général avec $pg=0$ et $K2=3,4$ (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 $K2=3$, ce qui suggère l'existence d'une relation particulière entre les surfaces de Keum–Naie satisfaisant $K2=3$ et $K2=4$.

Accepted:
Published online:
DOI: 10.1016/j.crma.2019.02.006
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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Park, Heesang; Shin, Dongsoo; Yang, Yoonjeong. Complex surfaces of general type with K2 = 3,4 and pg = q = 0. Comptes Rendus. Mathématique, Volume 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/

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[2] Keum, J. On Kummer Surfaces, University of Michigan, Ann Arbor, MI, USA, 1988 (PhD Thesis)

[3] J. Keum, Some new surfaces of general type with $pg=0$, 1988, unpublished manuscript.

[4] Mendes Lopes, M.; Pardini, R. Enriques surfaces with eight nodes, Math. Z., Volume 241 (2002), pp. 673-683

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

[6] Rito, C. Some bidouble planes with $pg=q=0$ and $4≤K2≤7$, Int. J. Math., Volume 26 (2015) no. 5

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