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Complex Hyperbolic Surfaces of Abelian Type

Holzapfel, R. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a Picard modular surface of...

Complex orientation formulas for M -curves of degree 4 d + 1 with 4 nests

S.Yu. Orevkov (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

On démontre la formule d’orientations complexes pour les M -courbes dans P 2 de degré 4 d + 1 ayant 4 nids. Cette formule généralise celle pour les M -courbes à nid profond. C’est un pas vers la classification des M -courbes de degré 9 .

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