Hilbert schemes, commuting matrices, and hyperkähler geometry

2019/03/05 by Roger Bielawski, Bielawski, Roger, Carolin Peternell +1
Mathematics · #14C05 #14H50 #53C26 #53C28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1903.01836

openalex publication_date 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We represent algebraic curves via commuting matrix polynomials. This allows us to show that the Hilbert scheme of cohomologically stable twisted rational curves of degree d in \Bbb P³\backslash \Bbb P¹ is isomorphic to a complexified hyperkähler quotient of an open subset of a vector space by a non-reductive Lie group.

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