论文标题
加权投影平面，Zariski对和合理的尖曲线的Cremona转换
Cremona transformations of weighted projective planes, Zariski pairs, and rational cuspidal curves
论文作者
论文摘要
在这项工作中，我们研究了加权射面的一个Cremona转换家族，该家族概括了投射平面的标准折痕转换。从特殊平面射击曲线开始，我们在具有特殊属性的加权射击平面中构建曲线家族。我们解释了如何使用Cremona转换的爆破分解来计算其补充的基本组，我们在加权射击平面中找到了Zariski对的示例（由Alexander多项式区分）。作为这种机械的另一种应用，我们研究了一个称为加权lê-yomdin的奇异家族，该家族提供了具有理性同源球体链接的表面奇点的无限示例。为了结束本文，我们还研究了一个表面奇点的家族，在不同方向上概括了Brieskorn-pham奇异性。这个家庭包含了许多整体同源领域链接的许多新示例，并回答了Némethi的一个问题。
In this work, we study a family of Cremona transformations of weighted projective planes which generalize the standard Cremona transformation of the projective plane. Starting from special plane projective curves we construct families of curves in weighted projective planes with special properties. We explain how to compute the fundamental groups of their complements, using the blow-up-down decompositions of the Cremona transformations, we find examples of Zariski pairs in weighted projective planes (distinguished by the Alexander polynomial). As another application of this machinery we study a family of singularities called weighted Lê-Yomdin, which provide infinite examples of surface singularities with a rational homology sphere link. To end this paper we also study a family of surface singularities generalizing Brieskorn-Pham singularities in a different direction. This family contains infinitely many new examples of integral homology sphere links, answering a question by Némethi.
