Numerical Kaehler-Einstein metric on the third del Pezzo

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dc.creatorDoran, C.
dc.creatorHeadrick, M.
dc.creatorHerzog, C. P.
dc.creatorKantor, J.
dc.creatorWiseman, T.
dc.date2007-03-07
dc.date2007-03-20
dc.date.accessioned2026-07-07T11:59:44Z
dc.date.available2026-07-07T11:59:44Z
dc.descriptionThe third del Pezzo surface admits a unique Kaehler-Einstein metric, which is not known in closed form. The manifold's toric structure reduces the Einstein equation to a single Monge-Ampere equation in two real dimensions. We numerically solve this nonlinear PDE using three different algorithms, and describe the resulting metric. The first two algorithms involve simulation of Ricci flow, in complex and symplectic coordinates respectively. The third algorithm involves turning the PDE into an optimization problem on a certain space of metrics, which are symplectic analogues of the "algebraic" metrics used in numerical work on Calabi-Yau manifolds. Our algorithms should be applicable to general toric manifolds. Using our metric, we compute various geometric quantities of interest, including Laplacian eigenvalues and a harmonic (1,1)-form. The metric and (1,1)-form can be used to construct a Klebanov-Tseytlin-like supergravity solution.
dc.description42 pages, 37 figures; v2 ref, preprint # added
dc.identifierhttps://arxiv.org/abs/hep-th/0703057
dc.identifierhttp://arxiv.org/abs/hep-th/0703057
dc.identifierCommun.Math.Phys.282:357-393,2008
dc.identifierdoi:10.1007/s00220-008-0558-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/206668
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.titleNumerical Kaehler-Einstein metric on the third del Pezzo
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