Asymptotically conical Ricci-flat Kähler metrics on C2 with cone singularities along a complex curve

Borbon, Martin de

doi:10.1112/jlms.12070

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Polyhedral Kähler Cones ([45]1

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2023

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“…The fact that Definition 2.1 is independent of the choice of adapted complex coordinates can be checked by a straightforward computation, writing z1 = fz 1 with f a non-vanishing holomorphic function, see page 3 in [15]. The metric g has an associated Kähler form ω that defines a closed current and therefore a de Rham cohomology class [ω].…”

Section: Organization Of the Papermentioning

confidence: 99%

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Calabi–Yau metrics with conical singularities along line arrangements

Borbon¹,

Spotti²

2023

J. Differential Geom.

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Given a finite collection of lines L j ⊂ CP 2 together with real numbers 0 < β j < 1 satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric g RF with cone angle 2πβ j along each line L j asymptotic to a polyhedral Kähler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of g RF as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.

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Section: Organization Of the Papermentioning

confidence: 99%

“…The radius function is homogeneous in complex coordinates. For every λ > 0 (15) r(λz, λw) = λ γ r(z, w), r∂ r = 1 γ Re (z∂ z + w∂ w ) .…”

Section: Polyhedral Kähler Cones ([45]mentioning

confidence: 99%