Demi-Normal Surface Singularities

TL;DR

This paper establishes methods to improve the singularities of Gorenstein demi-normal surfaces, achieving semi-rational and semi-log canonical models through normalization and gluing techniques.

Contribution

It introduces a process for semi-rationalification and semi-log canonicalization of Gorenstein demi-normal surfaces, extending singularity resolution techniques.

Findings

Existence of proper birational morphisms to semi-log canonical models.

Methodology involves normalization and gluing along the conductor.

Applicable to surfaces with semi-rational or semi-log canonical singularities.

Abstract

We prove semi-rationalification and semi-log-canonicalization for Gorenstein demi-normal surfaces. That is, given a Gorenstein demi-normal surface X with semi-rational (respectively, semi-log canonical) singularities in an open set U with complement a finite set of points, there is a proper birational morphism f : Y --> X such that f is an isomorphism over U and Y has only semi-rational (respectively, semi-log canonical) singularities. We proceed by passing to the normalization and then gluing along the conductor in an appropriate rationalification or log-canonicalization of the normalization of X.