Curvature formula for direct images of relative canonical bundles with a Poincaré type twist

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

Audience: researchers in the topic

Comments: We give a curvature formula of the L^2 metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed with a positive singular metric whose inverse has Poincaré type singularities along a relative snc divisor. The result applies to families of log canonically polarized pairs. Moreover, we show that it improves the general positivity result of Berndtsson-Paun in a special situation of a big line bundle.

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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