On Kobayashi's conjecture for K3 surfaces and hyperkähler manifolds
1 hour 1 min,
889.00 MB,
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About this item
| Description: |
Kamenova, L (Stony Brook University)
Monday 03 August 2015, 16:00-17:00 |
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| Created: | 2015-08-11 15:42 |
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| Collection: | Metric and Analytic Aspects of Moduli Spaces |
| Publisher: | Isaac Newton Institute |
| Copyright: | Kamenova, L |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincare disk to M is distance-decreasing. Kobayashi conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this conjecture for any hyperkahler manifold that admits a deformation with a Lagrangian fibration, and its Picard rank is not maximal. For hyperkahler manifolds with maximal Picard rank we need an extra assumption, the SYZ conjecture. We shall discuss the proof of Kobayashi's conjecture for K3 surfaces and for certain hyperkähler manifolds. These results are joint with S. Lu and M. Verbitsky. |
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