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Hirzebruch surfaces in a one–parameter family

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Abstract

We introduce a family of spaces, parametrized by positive real numbers, that includes all of the Hirzebruch surfaces. Each space is viewed from two distinct perspectives. First, as a leaf space of a compact, complex, foliated manifold, following Battaglia and Zaffran (Int Math Res Not 22:11785–11815, 2015). Second, as a symplectic cut of the manifold \(\mathbb C\times S^2\) in a possibly nonrational direction, following Battaglia and Prato (Int J Math 29:1850063, 2018).

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Acknowledgements

The research of the first two authors was partially supported by grant PRIN 2015A35N9B__013 (MIUR, Italy) and by GNSAGA (INdAM, Italy).

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Fiammetta Battaglia & Elisa Prato

  2. College of Marin, 835 College Ave, Kentfield, CA, 94904, USA

    Dan Zaffran

Authors
  1. Fiammetta Battaglia
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  2. Elisa Prato
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  3. Dan Zaffran
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Correspondence to Fiammetta Battaglia.

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Battaglia, F., Prato, E. & Zaffran, D. Hirzebruch surfaces in a one–parameter family. Boll Unione Mat Ital 12, 293–305 (2019). https://doi.org/10.1007/s40574-018-0181-1

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  • DOI: https://doi.org/10.1007/s40574-018-0181-1

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