Deformations of Nodal K\"ahler-Einstein Del Pezzo Surfaces with Discrete Automorphism Groups

TL;DR

This paper proves that small partial smoothings of certain nodal Kähler-Einstein Del Pezzo orbifolds with no holomorphic vector fields can be equipped with orbifold KE metrics close to the original, in the Gromov-Hausdorff sense.

Contribution

It establishes the existence of orbifold KE metrics on smoothings of nodal Del Pezzo orbifolds with discrete automorphism groups, extending KE metric theory.

Findings

Existence of orbifold KE metrics on small smoothings.

Metrics are close in the Gromov-Hausdorff sense.

Applicable to orbifolds with only nodal singularities and no holomorphic vector fields.

Abstract

In this paper we prove that generic small partial smoothings of Kahler-Einstein (KE) Del Pezzo orbifolds with only nodal singularities, and with no non-zero holomorphic vector fields, admit orbifold KE metrics which are close in the Gromov-Hausdorff sense to the original KE metric.