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arXiv · 1508.04634

On flops and canonical metrics

Ivan A. Cheltsov·Yanir A. Rubinstein
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Abstract

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.

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Ivan A. Cheltsov, Yanir A. Rubinstein. 2015-08-19. On flops and canonical metrics. https://doi.org/10.2422/2036-2145.201510_001

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