The Hilbert scheme of a pair of linear spaces is a Mori dream space

2020/06/11 by Ritvik Ramkumar, Ramkumar, Ritvik
Mathematics · #14D22 #14E05 #14E30 #14M15 #4C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2006.06211

openalex publication_date 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H_a,bⁿ denote the component of the Hilbert scheme whose general point parameterizes an a-plane union a b-plane meeting transversely in Pⁿ. We describe the effective and nef cones of H_a,bⁿ and determine when the component is Fano. Moreover, we show that H_a,bⁿ is a Mori dream space for all values of a,b,n.

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