This paper translates prior geometric conditions for invariant Kähler-Einstein metrics on cohomogeneity one G-manifolds into arithmetic properties of Koszul numbers for G equal to SU_n, Sp_n or Spin_n.
Calabi-Yau metrics on canonical bundles of flag varieties
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abstract
This note gives a simple formula for the unique asymptotically conical Calabi-Yau metrics on the canonical bundle of a flag variety known to exist by the work of R. Goto and others. This is done by generalizing the well known Calabi Ansatz to general K\"{a}hler classes. We give some examples of explicit families, in particular, a formula for the two dimensional family of asymptotically conical metrics on the canonical bundle of $F_{1,2}$.
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math.DG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Cohomogeneity one Kaehler and Kaehler-Einstein manifolds with one singular orbit, II
This paper translates prior geometric conditions for invariant Kähler-Einstein metrics on cohomogeneity one G-manifolds into arithmetic properties of Koszul numbers for G equal to SU_n, Sp_n or Spin_n.