Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

• Autorzy: Martin de Borbon
• Języki publikacji: EN

Abstrakty

EN

The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

Słowa kluczowe

EN

Kähler-Einstein metrics with cone singularities; Gromov-Hausdorff limits; Tangent cones

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 43-72

Daty

wydano

2017-02-01

otrzymano

2016-11-25

zaakceptowano

2017-02-28

online

2017-03-22

Twórcy

autor

Martin de Borbon

Identyfikatory

DOI

10.1515/coma-2017-0005