K\"ahler-Einstein metrics with conic singularities along self-intersecting divisors

TL;DR

This paper extends the theory of Kähler-Einstein metrics with conic singularities to include cases where the divisor has self-intersections, broadening the class of singularities that can be handled.

Contribution

It generalizes existing existence and regularity results for conic Kähler-Einstein metrics to normal crossing divisors with self-intersections.

Findings

Established existence of Kähler-Einstein metrics with conic singularities along self-intersecting divisors.

Proved regularity results for these metrics in the more general setting.

Extended previous theories to include more complex divisor configurations.

Abstract

In this paper, we extend the existence and regularity theorems for K\"ahler-Einstein metrics having conic singularities along a simple normal crossing divisor to the case of normal crossing divisor, i.e. when components of the divisor are allowed to intersect themselves transversely.