Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

By Frédéric Campana, Henri Guenancia, Mihai Puaun. 2011

135 citations recorded by the source corpus.

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved K\"ahler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/111b05f71aa1e9999e68a644788aaf818a3b259f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Orbifold generic semi-positivity: an application to families of canonically polarized manifolds (2013, result): “For similar results, we refer to [Ca09], and to [C-G-P 11], where transcendental methods are used.”
Smooth and singular Kahler-Einstein metrics (2014, methodology): “(iii) in the case Ricωφ = Ricω + √ −1∂∂̄ψ2 − √ −1∂∂̄ψ1 is due to Pǎun [196] (whose more quantitative formulation appears in [22,24]) together with Campana– Guenancia–Pǎun [52] that allows to assume only a lower bound on the bisectional curvature of the reference metric (without an upper bound on the”
Kahler-Einstein metrics with edge singularities (2011, background): “Both [15] and [16] appeared around the same time as the present article.”
K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, background): “X is smooth and D has simple normal crossings with coefficents <1, it follows the regularity results in [13,33] give that any log Kähler-Einstein metric for (X, D) has edge-cone singularities along D.”