Log canonical foliation singularities on surfaces

TL;DR

This paper classifies the dual graphs of exceptional divisors in minimal resolutions of log canonical foliation surface singularities and proves key properties like the ascending chain condition for minimal log discrepancies.

Contribution

It provides a classification of singularities and establishes foundational properties for foliated surface singularities, extending classical results to the foliated setting.

Findings

Classification of dual graphs for foliation singularities

Foliated minimal log discrepancies satisfy ascending chain condition

Grauert-Riemenschneider type vanishing theorem for foliated surfaces

Abstract

We give a classification of the dual graphs of the exceptional divisors on the minimal resolutions of log canonical foliation singularities on surfaces. For an application, we show the set of foliated minimal log discrepancies for foliated surface triples satisfies the ascending chain condition and a Grauert-Riemenschneider type vanishing theorem for foliated surfaces with good log canonical foliation singularities.