Notes on $\pi_1$ of Smooth Loci of Log Del Pezzo Surfaces

TL;DR

This paper investigates the finite fundamental groups of smooth loci of log del Pezzo surfaces, providing a comprehensive table and proofs for many of these groups, enhancing understanding of their algebraic topology.

Contribution

It offers a detailed classification and proof of the fundamental groups of smooth loci of log del Pezzo surfaces, including a comprehensive table of these groups.

Findings

Many groups are confirmed as fundamental groups.

A complete table of these groups is provided.

The study advances understanding of the topology of log del Pezzo surfaces.

Abstract

It is known that the fundamental groups of smooth loci of Log del Pezzo Surfaces are finite groups. The aim of this note is to study these finite groups. A short table containing these groups is given. And lots of groups on the table are proved to be fundamental groups.