1994/02/07 by Giorgio Ottaviani, Ottaviani, Giorgio, Günther Trautmann +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.alg-geom/9402005
openalex publication_date 1994/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mathematical instanton bundles on P3 have their analogues in rank--2n instanton bundles on odd dimensional projective spaces P2n+1. The families of special instanton bundles on these spaces generalize the special 'tHooft bundles on P3. We prove that for a special symplectic instanton bundle E on P2n+1 with c2=k h1End( E) = 4(3n-1) k + (2n-5)(2n-1). Therefore the dimension of the moduli space of instanton bundles grows linearly in k. The main difference with the well known case of P3 is that h2End( E) is nonzero, in fact we prove that it grows quadratically in k. Special symplectic instanton bundles turn out to be singular points of the moduli space. Such bundles E are SL(2)--invariant and the result is obtained regarding the cohomology groups of E as SL(2)--representations.