English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider an extension of the results of S. Bando, R. Kobyashi, G. Tian,and S. T. Yau on the existence of Ricci-flat K\"{a}hler metrics onquasi-projective varieties Y=X\D with \alpha[D]=c_1(X), \alpha >1. Therequirement that D admit a K\"{a}hler-Einstein metric is generalized to thecondition that the link S in the normal bundle of D admits a Sasaki-Einsteinstructure in the Sasaki-cone of the usual Sasaki structure provided theembedding D\subset X satisfies an additional holomorphic condition. If D is atoric variety, then S always admits a Sasaki-Einstein metric. As an applicationwe prove that every small smooth deformation of a toric Gorenstein singularityadmits a complete Ricci-flat K\"{a}hler metric asymptotic to a Calabi ansatzmetric. Some examples are given which were not previously known.

A Construction of Complete Ricci-flat K\"ahler Manifolds