Jet differentials on toroidal compactifications of ball quotients
Benoit Cadorel (IMT)
TL;DR
This paper provides explicit volume estimates for Green-Griffiths jet differentials on toroidal compactifications of ball quotients, advancing understanding of their geometric properties and growth behavior.
Contribution
It introduces a method to estimate the growth of logarithmic jet differentials and their vanishing conditions on these complex geometric structures.
Findings
Explicit volume estimates for jet differentials
Growth analysis of logarithmic jet spaces
Quantitative bounds on boundary vanishing conditions
Abstract
We give explicit estimates for the volume of the Green-Griffiths jet differentials of any order on a toroidal compactification of a ball quotient. To this end, we first determine the growth of the logarithmic Green-Griffiths jet differentials on these objects, using a natural deformation of the logarithmic jet space of a given order, to a suitable weighted projective bundle. Then, we estimate the growth of the vanishing conditions that a logarithmic jet differential must satisfy over the boundary to be a standard one.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology