K3曲面的组合性质：单纯形爆破和切片
Combinatorial properties of the K3 surface: Simplicial blowups and slicings
摘要：
具有16个节点的4维抽象库默簇K^4通过分解16个奇点而得到K3曲面。在这里，我们提出了一个简单的实现这个最小的决议。从K ^4的最小16顶点三角剖分开始，我们通过单纯性爆破一步一步地求解它的16个孤立奇点。作为结果，我们得到了一个17顶点三角剖分的标准PL K3曲面。关键的一步是构造一个三角形版本的映射柱的Hopf映射从真正的投影3-空间到2-球的顶点数最少。此外，我们还研究了单形Morse函数及其在临界点之间的能级变化。用这种方法我们得到了通过各种拓扑型的K3曲面的切片。
英文摘要：
The 4-dimensional abstract Kummer variety K^4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with a minimal 16-vertex triangulation of K^4 we resolve its 16 isolated singularities - step by step - by simplicial blowups. As a result we obtain a 17-vertex triangulation of the standard PL K3 surface. A key step is the construction of a triangulated version of the mapping cylinder of the Hopf map from the real projective 3-space onto the 2-sphere with the minimum number of vertices. Moreover we study simplicial Morse functions and the changes of their levels between the critical points. In this way we obtain slicings through the K3 surface of various topological types.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
