The tangent space at a special symplectic instanton bundle on P^{2n+1}

Abstract

Let $M{I}_{Simp,P^{2n+1}}(k)$ be the moduli space of stable symplectic instanton bundles on $P^{2n+1}$ with second Chern class $c_2=k$ (it is a closed subscheme of the moduli space $M{I}_{P^{2n+1}}(k)$), We prove that the dimension of its Zariski tangent space at a special (symplectic) instanton bundle is $2k(5n-1)+4n^2-10n+3,k\ge 2$. It follows that special symplectic instanton bundles are smooth points for $k\le 3$

arXiv commentLatex, 11 pages, to appear in Annali di Matematica