Duke Mathematical Journal
- Duke Math. J.
- Volume 162, Number 15 (2013), 2855-2902.
Asymptotically conical Calabi–Yau manifolds, I
This is the first of a series of articles on complete Calabi–Yau manifolds asymptotic to Riemannian cones at infinity. We begin by proving general existence and uniqueness results. The uniqueness part relaxes the decay condition needed in earlier work to , relying on some new ideas about harmonic functions. We then look at two classes of examples: crepant resolutions of cones (this includes a new class of Ricci-flat small resolutions associated with flag varieties) and affine deformations of cones. One focus here is the question of the precise rate of decay of the metric to its tangent cone. We prove that the optimal rate for the Stenzel metric on is .
Duke Math. J., Volume 162, Number 15 (2013), 2855-2902.
First available in Project Euclid: 28 November 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 14J32: Calabi-Yau manifolds
Conlon, Ronan J.; Hein, Hans-Joachim. Asymptotically conical Calabi–Yau manifolds, I. Duke Math. J. 162 (2013), no. 15, 2855--2902. doi:10.1215/00127094-2382452. https://projecteuclid.org/euclid.dmj/1385661570