Warped quasi-asymptotically conical Calabi-Yau metrics

Abstract: We will explain how to construct new examples of complete Calabi-Yau manifolds of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones. A description of the geometry at infinity will be given in terms of a compactification by a manifold with corners obtained through a suitable sequence of blow-ups. A key analytical step in the construction of these Calabi-Yau metrics is to derive good mapping properties of the Laplacian on some suitable weighted Hölder spaces. Our methods also produce Calabi-Yau metrics with an isolated conical singularity modelled on a Calabi-Yau cone distinct from the tangent cone at infinity, in particular yielding a transition behavior between different Calabi-Yau cones as conjectured by Yang Li. This is used to exhibit many examples where the tangent cone at infinity does not uniquely specify a Calabi-Yau metric with exact Kähler form. This is a joint work with Ronan Conlon.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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