Weighted K-stability of polarized varieties and extremality of Sasaki\n manifolds
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Bibliographic record
Abstract
We use the correspondence between extremal Sasaki structures and weighted\nextremal Kahler metrics defined on a regular quotient of a Sasaki manifold,\nestablished by the first two authors, and Lahdili's theory of weighted\nK-stability in order to define a suitable notion of (relative) weighted\nK-stability for compact Sasaki manifolds of regular type. We show that the\n(relative) weighted K-stability with respect to a maximal torus is a necessary\ncondition for the existence of a (possibly irregular) extremal Sasaki metric.\nWe also compare weighted K-stability to the K-stability of the corresponding\npolarized affine cone (introduced by Collins-Szekelyhidi), and prove that they\nagree on the class of test configurations we consider. As a byproduct, we\nstrengthen the obstruction to the existence of a scalar-flat Kahler cone metric\nfrom the K-semistability to the K-stability on these test configurations. We\nuse our approach to give a characterization of the existence of a compatible\nextremal Sasaki structure on a principal circle bundle over an admissible ruled\nmanifold, expressed in terms of the positivity of a single polynomial of one\nvariable over a given interval.\n
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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