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Hilbert schemes of some threefold scrolls over 𝔽e

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

Abstract

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


Acknowledgements

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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