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Kähler–Einstein metrics with prescribed singularities on Fano manifolds [PDF]
Journal für die Reine und Angewandte Mathematik, 2020 Given a Fano manifold ( X , ω ) {(X,\omega)} , we develop a variational approach to characterize analytically the existence of Kähler–Einstein metrics with prescribed singularities, assuming that these singularities can be approximated algebraically ...
Antonio Trusiani
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Continuity of delta invariants and twisted K\"ahler--Einstein metrics. [PDF]
, 2020 We show that delta invariant is a continuous function on the big cone. We will also introduce an analytic delta invariant and show its continuity in the Kahler cone, from which we deduce the continuity of the greatest Ricci lower bound.
Kewei Zhang
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Einstein metrics on spheres [PDF]
Annals of Mathematics, 2005 19 pages, some references added and clarifications made.
Boyer, Charles P. +2 more
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Singular Kähler-Einstein metrics [PDF]
Journal of the American Mathematical Society, 2009 We study degenerate complex Monge-Ampère equations of the form ( ω
Eyssidieux, Philippe +2 more
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Geometry of Twisted Kähler–Einstein Metrics and Collapsing [PDF]
Communications in Mathematical Physics, 2019 We prove that the twisted Kähler–Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi–Yau fibers have conical-type singularities along the discriminant locus.
M. Gross +2 more
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Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique, 2022 This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles.
Bi, Enchao, Hou, Zelin
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Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for vector bundles [PDF]
Épijournal de Géométrie Algébrique, 2022 For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics.
Yoshinori Hashimoto, Julien Keller
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Homogeneous Einstein metrics and butterflies
Annals of Global Analysis and Geometry, 2023 M.~M.~Graev associated in \cite{Gr} to a compact homogeneous space $G/H$ a nerve $\XGH$, whose non-contractibility implies the existence of a $G$-invariant Einstein metric on $G/H$. The nerve $\XGH$ is a compact semi-algebraic set, defined purely Lie theoretically by intermediate subgroups. In this paper we present a detailed description of the work of
Christoph Böhm, Megan M. Kerr
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Stability of Einstein metrics on homogeneous spaces [PDF]
, 2023 (1) Stability of Einstein metrics on symmetric spaces of compact type: We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces SU(n), n ≥ 3, and E_6/F_4 .
Schwahn, Paul
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Kähler–Einstein metrics on orbifolds and Einstein metrics on spheres
Commentarii Mathematici Helvetici, 2007 A construction of Kähler–Einstein metrics using Galois coverings, studied by Arezzo–Ghigi–Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of ℂℙ^n which are trivial set theoretically, one obtains new Einstein metrics on
GHIGI, ALESSANDRO CALLISTO, Kollar, J.
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