Positivity in Kähler-Einstein theory

Gabriele Di Cerbo, Luca F. Di Cerbo

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Tian initiated the study of incomplete Kähler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor, described by the cone-angle 2π(1-α) for αε (0, 1). In this paper we study how the existence of such Kähler-Einstein metrics depends on α. We show that in the negative scalar curvature case, if such Kähler-Einstein metrics exist for all small cone-angles then they exist for every αε((n+1)/(n+2), 1), where n is the dimension. We also give a characterisation of the pairs that admit negatively curved cone-edge Kähler-Einstein metrics with cone angle close to 2π. Again if these metrics exist for all cone-angles close to 2π, then they exist in a uniform interval of angles depending on the dimension only. Finally, we show how in the positive scalar curvature case the existence of such uniform bounds is obstructed.

Original languageEnglish (US)
Pages (from-to)321-338
Number of pages18
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
StatePublished - Sep 4 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics


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