Asymptotically cylindrical steady Kähler-Ricci solitons

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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