Calabi-Yau metrics on canonical bundles of flag varieties

2018/07/19 by van Coevering, Craig
#32M10 (Secondary) #32Q20 #53C25 (Primary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.07256

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 Kähler 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.

Related

• Calabi-Yau metrics on canonical bundles of complex flag manifolds
• Calabi-Yau metrics of Calabi type with polynomial rate of convergence
• On the degeneration of asymptotically conical Calabi-Yau metrics
• Warped quasi-asymptotically conical Calabi-Yau metrics
• Asymptotically conical Calabi-Yau metrics on quasi-projective varieties