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Conformally Kähler, Einstein–Maxwell metrics on Hirzebruch surfaces

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0 Published in 2020 at "Annals of Global Analysis and Geometry"

DOI: 10.1007/s10455-020-09749-y

Abstract: In this note, we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono [ 18 ], gives rise to new conformally Kähler, Einstein–Maxwell metrics. The correspondent… read more here.

Keywords: metrics hirzebruch; hler einstein; einstein maxwell; hirzebruch surfaces ... See more keywords

Kähler–Einstein metrics and volume minimization

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0 Published in 2019 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2018.10.038

Abstract: We prove that if a $\mathbb{Q}$-Fano variety $V$ specially degenerates to a K\"{a}hler-Einstein $\mathbb{Q}$-Fano variety $V$, then for any ample Cartier divisor $H=-r^{-1} K_V$ with $r\in \mathbb{Q}_{>0}$, the normalized volume $\widehat{\rm vol}(v)=A_{\mathcal{C}}^n(v)\cdot {\rm vol}(v)$ is… read more here.

Keywords: einstein metrics; hler einstein; einstein; metrics volume ... See more keywords

The volume of singular Kähler–Einstein Fano varieties

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1 Published in 2018 at "Compositio Mathematica"

DOI: 10.1112/s0010437x18007042

Abstract: We show that the anti-canonical volume of an $n$ -dimensional Kähler–Einstein $\mathbb{Q}$ -Fano variety is bounded from above by certain invariants of the local singularities, namely $\operatorname{lct}^{n}\cdot \operatorname{mult}$ for ideals and the normalized volume function… read more here.

Keywords: einstein fano; hler einstein; fano varieties; volume ... See more keywords

Deformation for coupled Kähler–Einstein metrics

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0 Published in 2021 at "Journal of The Mathematical Society of Japan"

DOI: 10.2969/jmsj/84408440

Abstract: The notion of coupled Kähler-Einstein metrics was introduced recently by Hultgren-WittNyström. In this paper we discuss deformation of a coupled KählerEinstein metric on a Fano manifold. We obtain a necessary and sufficient condition for a… read more here.

Keywords: coupled hler; hler einstein; deformation coupled;