2009/06/10 by Daniele Faenzi, Faenzi, Daniele, Maria Lucia Fania +1
Mathematics · #14E05 #14J40 #14M12 #14N15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14E05 #msc:14J40 #msc:14M12 #msc:14N15
paper · pdf · doi:10.48550/arxiv.0906.1875
Revised version, to appear in Math. Ann
openalex publication_date 2009/06/10 · arxiv created 2009/11/23 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that, for m greater than 3 and k greater than m-2, the Grassmannian of m-dimensional subspaces of the space of skew-symmetric forms over a vector space of dimension 2k is birational to the Hilbert scheme of Palatini scrolls in P^(2k-1). For m=3 and k greater than 3, this Grassmannian is proved to be birational to the set of pairs (E,Y), where Y is a smooth plane curve of degree k and E is a stable rank-2 bundle on Y whose determinant is O(k-1).