Hilbert scheme of some threefold scrolls over the Hirzebruch surface F₁

2011/10/25 by Gian Mario Besana, Besana, Gian Mario, Maria Lucia Fania +3 · 1 citation
Mathematics · #14J30 #14M07 #14N25 (Primary) 14N30 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14J30 #msc:14M07 #msc:14N25 #msc:14N30

paper · pdf · doi:10.48550/arxiv.1110.5464

23 pages; title changed, as suggested by the referee; elementary transformation approach contained in new Section 4, as suggested by the refeeree; to appear in Journal of the Mathematical Society of Japan

openalex publication_date 2011/10/25 · arxiv created 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hilbert schemes of suitable smooth, projective manifolds of low degree which are 3-fold scrolls over the Hirzebruch surface F₁ 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.

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