ON GENERATING LOOPS OF THE LINK OF A WAHL SINGULARITY

• 발행기관: 충청수학회
• 저자명: Yonghwa Cho
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 38, No. 3, 199~209쪽, 전체 11쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2025.08.31

국문 초록

Let us consider the first homology group H (L, Z) of the link of a Wahl singularity. According to Mumford, H (L, Z) is generated by suitably oriented loops around the exceptional curves in the minimal resolution. It can be easily seen that the loop around one of the end branches of the exceptional curves generates H (L, Z). However, it is not always true that the loop around an intermediate curve generates H (L, Z). In this article, we define a special intermediate curve (which we call an ancestor ) in the chain of exceptional curves, and prove the the loop around the ancestor generates H (L, Z). This can be applied to the construction of exceptional vector bundles on Dolgachev surfaces which are constructed via Q-Gorenstein smoothing.

목차

1. Introduction

2. Proof

3. Application to exceptional vector bundles on Dolgachev surfaces

References

키워드

Wahl singularity Hirzebruch-Jung continued fraction link