Rigidity and vanishing of basic Dolbeault cohomology of Sasakian manifolds

Goertsches, Oliver; Nozawa, Hiraku; Toeben, Dirk

doi:10.48550/arxiv.1206.2803

Cited by 1 publication

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“…Now, we have the following important theorem: in the positive Sasakian case, the (p, 0)th and (0, q)th Hodge number vanishing for p > 0 and q > 0 [51]. In the quasi-regular case, they are just the Hodge number of orbifold (S, ∆) [51]. So essentially the only nonzero basic Hodge numbers are (h 0,0 , h 1,1 ).…”

Section: Now We Can Decompose Every Form As Followsmentioning

confidence: 96%

“…Each basic p form also has a Hodge decomposition, and the dimension of harmonic solution is called basic Hodge number. Now, we have the following important theorem: in the positive Sasakian case, the (p, 0)th and (0, q)th Hodge number vanishing for p > 0 and q > 0 [51]. In the quasi-regular case, they are just the Hodge number of orbifold (S, ∆) [51].…”

Section: Now We Can Decompose Every Form As Followsmentioning

confidence: 97%

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Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I

Xie¹,

Yau²

2019

Preprint

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A five dimensional Sasaki-Einstein (SE) manifold provides a AdS/CFT pair for four dimensional N = 1 SCFT, and those pairs are very useful in studying field theory and AdS/CFT correspondence. The space of known SE manifolds is increased significantly in the last decade, and we initiated the study of various field theory properties through the geometric property of these new SE manifolds. There is an associated three dimensional log-terminal singularity X for each SE manifold L X , and for quasi-regular case, there is an associated two dimensional log Del Pezzo surface (S, ∆). The algebraic geometrical methods are quite useful in extracting interesting physical properties from singularity and log Del Pezzo surface. The necessary and sufficient condition for the existence of SE metric on L X is related to K stability of X. Motivated by dual field theory, we propose a conjecture on how to reduce the check of K stability to possibly finite cases, which hopefully would give us a guideline to find a much larger space of SE metrics.

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Section: Now We Can Decompose Every Form As Followsmentioning

confidence: 96%

Section: Now We Can Decompose Every Form As Followsmentioning

confidence: 97%