Journal of the Mathematical Society of Japan

Hilbert scheme of some threefold scrolls over the Hirzebruch surface ${\mathbb F}_1$

Gian Mario BESANA, Maria Lucia FANIA, and Flaminio FLAMINI

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Hilbert schemes of suitable smooth, projective manifolds of low degree which are 3-fold scrolls over the Hirzebruch surface $\mathbb{F}_1$ 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.

Article information

J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1243-1272.

First available in Project Euclid: 24 October 2013

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Zentralblatt MATH identifier

Primary: 14J30: $3$-folds [See also 32Q25] 14M07: Low codimension problems 14N25: Varieties of low degree
Secondary: 14N30: Adjunction problems

Hilbert scheme special threefolds vector bundles ruled varieties


BESANA, Gian Mario; FANIA, Maria Lucia; FLAMINI, Flaminio. Hilbert scheme of some threefold scrolls over the Hirzebruch surface ${\mathbb F}_1$. J. Math. Soc. Japan 65 (2013), no. 4, 1243--1272. doi:10.2969/jmsj/06541243.

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