Research profile

Mark Gross

Works on analytic minimal model program, Ricci-flat & Calabi–Yau and Kähler–Einstein & K-stability.

NP-RC-436880

10
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2
co-authors
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Analytic minimal model programRicci-flat & Calabi–YauKähler–Einstein & K-stabilityKähler–Ricci flow(Non)collapsingEinstein metricsLimit spaces & RCDKähler geometry

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  1. Valentino Tosatti

    1 joint worklatest 2019

  2. Yuguang Zhang

    1 joint worklatest 2019

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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.

2019

math.DGv2arXiv:1911.07315

Geometry of twisted Kähler-Einstein metrics and collapsing

Mark Gross, Valentino Tosatti, Yuguang Zhang

We prove that the twisted Kahler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when studying the collapsing of Ricci-flat Kahler metrics on Calabi-Yau manifolds, and of the Kahler-Ricci flow on compact Kahler manifolds with semiample canonical bundle and intermediate Kodaira dimension. Our results allow us to understand their collapsed Gromov-Hausdorff limits when the base is smooth and the discriminant has simple normal crossings.

Ricci flowKähler–Ricci flowEinstein metricsRicci-flat & Calabi–YauSingularities(Non)collapsingKähler geometryLimit spaces & RCDKähler–Einstein & K-stabilityAnalytic minimal model program
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