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Hilbert schemes of some threefold scrolls over 𝔽e

  • Maria Lucia Fania EMAIL logo and Flaminio Flamini
From the journal Advances in Geometry


Hilbert schemes of suitable smooth, projective threefold scrolls over the Hirzebruch surface 𝔽e, e ≥ 2, are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension, and the general point of such a component is described.

Communicated by: A. Sommese


The authors thank C. Ciliberto and E. Sernesi for having pointed out questions on Hilbert schemes of threefold scrolls over 𝔽e, with e ≥ 2, during the talk of the first author at the Workshop “Algebraic geometry: two days in Rome two”, held in Rome in February 2012. The authors are also grateful to the referee for helpful comments and for having posed a question which allowed us to realize that there was a mistake in the first version of the paper. Both authors are members of GNSAGA-INdAM.

Funding: We acknowledge partial support from MIUR funds, PRIN 2010-2011 project “Geometria delle Varietà Algebriche”.


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Received: 2014-7-9
Revised: 2015-1-19
Revised: 2015-4-21
Published Online: 2016-10-14
Published in Print: 2016-10-1

© 2016 by Walter de Gruyter Berlin/Boston

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