Carathéodory measure hyperbolicity and positivity of canonical bundles
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- by Shin Kikuta PDF
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Abstract:
In this paper, we prove that the curvature of the Carathéodory pseudo-volume form is bounded above by $-1$. On the set where the pseudo-volume form is non-degenerate, the curvature current of the singular Hermitian metric associated with the Carathéodory pseudo-volume form is proved to be strictly positive. Due to these curvature properties, we obtain an explicit relation between the Carathéodory measure hyperbolicity and the positivity of the canonical bundle. Moreover, we show a relation between the Carathéodory measure hyperbolicity, the existence of the Bergman kernel form and the existence of the Bergman metric.References
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Additional Information
- Shin Kikuta
- Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
- Email: sa6m15@math.tohoku.ac.jp
- Received by editor(s): November 4, 2009
- Received by editor(s) in revised form: April 20, 2010, and April 28, 2010
- Published electronically: September 1, 2010
- Communicated by: Franc Forstneric
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1411-1420
- MSC (2010): Primary 32Q45; Secondary 32J18, 32J25
- DOI: https://doi.org/10.1090/S0002-9939-2010-10564-6
- MathSciNet review: 2748434