On the maximum number of complexes of a given degree containing subvarieties of Grassmannians

2023/04/14 by Ciro Ciliberto, Ciliberto, Ciro
Mathematics · Medicine · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Graph theory and applications #Phytoestrogen effects and research

paper · pdf · doi:10.48550/arxiv.2304.07053

openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \G(k,r) be the Grassmannian of k--subspaces in \Proj^r embedded in \Proj^N(k,r), with N(k,r)=r+1\choose k+1-1, via the Plücker embedding. In this paper, extending some classical results by Gallarati (see \cite Gal1,Gal2), we give a sharp upper bound for the number of independent sections of H⁰(\G(k,r), Ø_\G(k,r)(m)) vanishing on a subvariety X of \G(k,r) such that the union of the k--subspaces corresponding to the points of X spans \Proj^r.

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