Construction of hyperbolic Horikawa surfaces

Liu, Yuchen

Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 541-561.

Nous construisons une surface de Horikawa Brody-hyperbolique qui est un revêtement double de ${\mathbb{P}}^2$ ramifié le long d’une courbe lisse de degré 10. Nous construisons également des surfaces Brody-hyperboliques qui sont des revêtements doubles de surfaces de Hirzebruch, dont l’ensemble de ramification est de bidegré minimal.

We construct a Brody hyperbolic Horikawa surface that is a double cover of ${\mathbb{P}}^2$ branched along a smooth curve of degree 10. We also construct Brody hyperbolic double covers of Hirzebruch surfaces with branch loci of the lowest possible bidegree.

Classification : 32Q45, 14J29
Keywords: Brody hyperbolicity, Horikawa surfaces, cyclic covers
Mot clés : Hyperbolicité au sens de Brody, surface de Horikawa, revêtements cycliques

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