We consider Fano manifolds M that admit a collection of finite automorphism groups G_1, ..., G_k such that the quotients M/G_i are smooth Fano manifolds possessing a Kaehler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kaehler-Einstein metric too.
Arezzo, C., Ghigi, A., Pirola, G. (2006). Symmetries, quotients and Kaehler-Einstein metrics. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 591(591), 177-200 [10.1515/CRELLE.2006.018].
Symmetries, quotients and Kaehler-Einstein metrics
GHIGI, ALESSANDRO CALLISTO;
2006
Abstract
We consider Fano manifolds M that admit a collection of finite automorphism groups G_1, ..., G_k such that the quotients M/G_i are smooth Fano manifolds possessing a Kaehler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kaehler-Einstein metric too.
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