The tangent space at a special symplectic instanton bundle on P²ⁿ⁺¹

1997/07/10 by Carla Dionisi, Dionisi, Carla
Mathematics · #14D20 (Primary) 14F05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG #msc:14D20 #msc:14F05

paper · pdf · doi:10.48550/arxiv.alg-geom/9707011

Latex, 11 pages, to appear in Annali di Matematica

arxiv created 1997/07/10 · openalex publication_date 1997/07/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let MI_{Simp,P²ⁿ⁺¹}(k) be the moduli space of stable symplectic instanton bundles on P²ⁿ⁺¹ with second Chern class c₂=k (it is a closed subscheme of the moduli space MI_P²ⁿ⁺¹(k)), We prove that the dimension of its Zariski tangent space at a special (symplectic) instanton bundle is 2k(5n-1)+4n²-10n+3, k≥ 2. It follows that special symplectic instanton bundles are smooth points for k ≤ 3

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