Hirzebruch surfaces in a one–parameter family

  • Fiammetta BattagliaEmail author
  • Elisa Prato
  • Dan Zaffran


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).



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

Compliances with ethical standard

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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© Unione Matematica Italiana 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Informatica “U. Dini”Università di FirenzeFirenzeItaly
  2. 2.College of MarinKentfieldUSA

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