Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages

Collection Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages

Organizer(s) Brotbek, Damian ; Diverio, Simone ; Gasbarri, Carlo ; Rousseau, Erwan

Date(s) 18/02/2019 - 22/02/2019

linked URL https://conferences.cirm-math.fr/2102.html

00:00:00 / 00:00:00

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Special manifolds, the core fibration, rational and entire curves

By Frédéric Campana

For complex projective manifolds $X$ of general type, Lang claimed the equivalence between three fields: birational geometry, complex hyperbolicity, and arithmetic. We extend this equivalence to arbitrary $X$’s by introducing the (antithetical) class of “Special” manifolds and constructing the “Core” fibration, the unique one with special fibres and general type “orbifold” base. We conjecture that special manifolds —which are defined algebro-geometrically by a certain non-positivity of their cotangent bundles— are also exactly the ones having Zariski-dense entire curves (so violating the GGL property). We shall give (j.w. J. Winkelmann) some examples supporting this conjecture. The arithmetic aspect will be skipped.

Information about the video

Date of recording 21/02/2019
Date of publication 28/02/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19495303
Cite this video Campana, Frédéric (21/02/2019). Special manifolds, the core fibration, rational and entire curves. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19495303
URL https://dx.doi.org/10.24350/CIRM.V.19495303

Domain(s)

Bibliography

Campana, F., & Winkelmann, J. (2015). On the h-principle and specialness for complex projective manifolds. Algebraic Geometry, 2(3), 298-314 - https://doi.org/10.14231/AG-2015-013

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