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首页> 外文期刊>Journal of geometry and symmetry in physics >WEAK FORM OF HOLZAPFEL'S CONJECTURE
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WEAK FORM OF HOLZAPFEL'S CONJECTURE

机译：HOLZAPFEL的虚构形式

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摘要

Let B C~2 be the unit ball and I' be a lattice of SU(2, 1). Bearing in mind that all compact Riemann surfaces are discrete quotients of the unit disc A C C, Holzapfel conjectures that the discrete ball quotients B/Г and their compactifications are widely spread among the smooth projective surfaces. There are known ball quotients B/Г of general type, as well as rational, abelian, K3 and elliptic ones. The present note constructs three non-compact ball quotients, which are birational, respectively, to a hyperelliptic, Enriques or a ruled surface with an elliptic base. As a result, we establish that the ball quotient surfaces have representatives in any of the eight Enriques classification classes of smooth projective surfaces.
机译：设B C〜2为单位球，I'为SU（2，1）的晶格。考虑到所有紧致的黎曼曲面都是单位圆盘A C C的离散商，Holzapfel猜想，离散球商B /Г及其压实度在光滑的投影表面之间广泛分布。已知一般类型的球商B /Г以及有理，阿贝尔，K3和椭圆的商。本说明构造了三个非紧实的球商，它们分别是双椭圆的，超椭圆的，恩里克或具有椭圆底的直纹表面。结果，我们确定球商曲面在光滑投影曲面的八个Enriques分类类别中的任何一个中都有代表。

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