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On symmetries of transversely projective foliations

By Federico Lo Bianco

Appears in collection : Jean-Morlet Chair 2020 - Research School: Geometry and Dynamics of Foliations / Chaire Jean-Morlet 2020 - Ecole : Géométrie et dynamiques des feuilletages

We consider a holomorphic (singular) foliation F on a projective manifold X and a group G of birational transformations of X which preserve F (i.e. it permutes the set of leaves). We say that the transverse action of G is finite if some finite index subgroup of G fixes each leaf of F.In a joint work with J. V. Pereira, E. Rousseau and F. Touzet, we show finiteness for the group of birational transformations of general type foliations with tame singularities and transverse finiteness for (non-virtually euclidean) transversely projective foliations. In this talk I will focus on the latter result, time permitting, I will show how the presence of a transverse structure (projective, hyperbolic, spherical...) and the analysis of the resulting monodromy representation allow to reduce to the case of modular foliations on Shimura varieties and to conclude.

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Citation data

  • DOI 10.24350/CIRM.V.19638003
  • Cite this video Lo Bianco Federico (5/25/20). On symmetries of transversely projective foliations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19638003
  • URL https://dx.doi.org/10.24350/CIRM.V.19638003

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Bibliography

  • BIANCO, F. Lo, ROUSSEAU, Erwan, et TOUZET, Frédéric. Symmetries of Transversely Projective Foliations. arXiv preprint arXiv:1901.05656, 2019. - https://arxiv.org/abs/1901.05656

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