Mathematical Research Letters

Volume 20 (2013)

Number 3

A remark on conical Kähler-Einstein metrics

Pages: 581 – 590



Gábor Székelyhidi (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)


We give some non-existence results for Kähler-Einstein metrics with conical singularities along a divisor on Fano manifolds. In particular, we show that the maximal possible cone angle is in general smaller than the invariant $R(M)$. We study this discrepancy from the point of view of log $K$-stability.

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