Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections

Tomohiro Okuma

Journal of Singularities
volume 23 (2021), 170-193

Received: 21 March 2021. Received in revised form: 28 July 2021.

DOI: 10.5427/jsing.2021.23j

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Abstract:

For a given topological type of a normal surface singularity, there are various types of complex structures which realize it. We are interested in the following problem: Find the maximum of the geometric genus and a condition for that the maximal ideal cycle coincides with the fundamental cycle on the minimal good resolution. In this paper, we study weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersection singularities from the perspective of the problem.

2000 Mathematical Subject Classification:

Primary 32S25; Secondary 14J17, 32S05, 14B05

Key words and phrases:

Surface singularities, weighted homogeneous singularities, Brieskorn complete intersections, geometric genus, maximal ideal cycles

Author(s) information:

Tomohiro Okuma
Department of Mathematical Sciences
Yamagata University
Yamagata 990-8560, Japan
email: okuma@sci.kj.yamagata-u.ac.jp