Log canonical thresholds of certain Fano hypersurfaces
Ivan Cheltsov, Jihun Park, Joonyeong Won
TL;DR
This paper investigates the log canonical thresholds of specific Fano hypersurfaces, such as quartic threefolds and quintic fourfolds, demonstrating that general cases admit Kähler-Einstein metrics.
Contribution
It provides new calculations of log canonical thresholds for certain Fano hypersurfaces and establishes conditions for the existence of Kähler-Einstein metrics in these cases.
Findings
Log canonical thresholds are computed for quartic threefolds and quintic fourfolds.
General Fano hypersurfaces in these classes admit Kähler-Einstein metrics.
Results contribute to understanding stability and metric properties of Fano varieties.
Abstract
We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an application, we show that they have a Kaehler-Einstein metric if they are general.
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