Chern numbers ratios of surfaces with big cotangent bundle

Abstract: Bigness of the cotangent bundle of a projective manifold is the condition that the growth of the space of sections of the symmetric powers of the cotangent bundle is maximal. The condition implies that the manifold is of general type, that is, its canonical bundle $K_X$ satisfies the same condition. If an algebraic surface $X$ has a big cotangent bundle, then $X$ satisfies Green-Griffiths-Lang conjecture. This talk examines the implication of our CMS-criterion for bigness of the cotangent  bundle, a condition about numerical invariants of $X$, towards the possible ratios of the Chern numbers $c_1^2=K_X^2$ and $c_2=\xi_{top}(X)$ of surfaces $X$ with big cotangent bundle. We present several conjectures concerning  these ratios motivated by the CMS-criterion and  examples supporting the conjectures.

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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