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On invariance of plurigenera for foliations on surfaces

  • Paolo Cascini ORCID logo EMAIL logo and Enrica Floris
Published/Copyright: March 22, 2016

Abstract

We show that if (Xt,t)tΔ is a family of foliations with reduced singularities on a smooth family of surfaces, then invariance of plurigenera h0(Xt,mKt) holds for sufficiently large m. On the other hand, we provide examples on which the result fails, for small values of m.

Award Identifier / Grant number: P40216

Funding statement: Both the authors were partially supported by an EPSRC grant (P40216).

Acknowledgements

We would like to thank Y. Gongyo, J. V. Pereira, M. McQuillan, R. Pignatelli and H. Tanaka for several very useful discussions and comments. The work started as an attempt to answer a question raised by J. V. Pereira during the workshop “Foliation theory in algebraic geometry” supported by the Simons foundation. We would like to thank the referee for carefully reading our manuscript, for suggesting several improvements and for pointing out some errors in an earlier version of this paper.

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Received: 2015-02-13
Revised: 2015-11-19
Published Online: 2016-03-22
Published in Print: 2018-11-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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