Schäfer, Johannes (2021) Asymptotically cylindrical steady Kähler-Ricci solitons. MPIM Preprint Series 2021 (10).
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Abstract
Let $D$ be a compact Kähler manifold with trivial canonical bundle and $\Gamma$ be a finite cyclical group of order $m$ acting on $\mathbb{C} \times D$ by biholomorphisms, where the action on the first factor is generated by rotation of angle $2\pi /m$. Furthermore, suppose that $\Omega_D$ is a trivialisation of the canonical bundle such that $\Gamma$ preserves the holomorphic form $dz \wedge \Omega_D$ on $\mathbb C \times D$, with $z$ denoting the coordinate on $\mathbb{C}$.
The main result of this article is the construction of new examples of gradient steady Kähler-Ricci solitons on certain crepant resolutions of the orbifolds $\left( \mathbb{C}\times D \right) / \Gamma$. These new solitons converge exponentially to a Ricci-flat cylinder $\mathbb{R} \times(\mathbb{S}^1 \times D) / \Gamma$.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 3 Geometry and topology > 51-XX Geometry |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 31 Mar 2021 09:55 |
| Last Modified: | 25 Apr 2021 17:25 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4528 |
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