Nondegenerate multidimensional matrices and instanton bundles

2001/03/13 by Laura Costa, Giorgio Ottaviani, Costa, Laura +1
Mathematics · #14D21 #14J60 #15A72 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14D21 #msc:14J60 #msc:15A72

paper · pdf · doi:10.48550/arxiv.math/0103078

9 pages, Latex 2e

arxiv created 2001/03/13 · openalex publication_date 2001/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that the moduli space of rank 2n symplectic instanton bundles on \PP²ⁿ⁺¹, defined from the well known monad condition, is affine. This result was not known even in the case n=1, where the real instanton bundles correspond to self dual Yang Mills Sp(1)-connections over the 4-dimensional sphere. The result is proved as a consequence of the existence of an invariant of the multidimensional matrices representing the instanton bundles.

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