On flops and canonical metrics

Ivan A. Cheltsov, Yanir A. Rubinstein

Research output: Contribution to journalArticlepeer-review


This article is concerned with an observation for proving non-existence of canonical Kahler metrics. The idea is to use a rather explicit type of degeneration that applies in many situations. Namely, in a variation on a theme introduced by Ross-Thomas, we consider flops of the deformation to the normal cone. This yields a rather widely applicable notion of stability that is still completely explicit and readily computable, but with wider scope. We describe some applications, among them, a proof of one direction of the Calabi conjecture for asymptotically logarithmic del Pezzo surfaces.
Original languageEnglish
Pages (from-to)283-311
Journalannali della scuola normale di pisa
Issue number1
Publication statusPublished - 29 Mar 2018


  • math.AG
  • math.DG
  • 14E05, 32Q25 (Primary), 14J45, 53C25, 53C55 (Secondary)

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