Moduli of mathematical instanton vector bundles with odd c_2 on projective space

The problem of irreducibility of the moduli space I_n of rank-2 mathematical instanton vector bundles with arbitrary positive second Chern class n on the projective 3-space is considered. The irreducibility of I_n was known for small values of n: Barth 1977 (n=1), Hartshorne 1978 (n=2), Ellingsrud and Stromme 1981 (n=3), Barth 1981 (n=4), Coanda, Tikhomirov and Trautmann 2003 (n=5). In this paper we prove the irreducibility of I_n for an arbitrary odd n.Comment: 62 page

Moduli of symplectic instanton vector bundles of higher rank on projective space P3

Symplectic instanton vector bundles on the projective space P3 constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space In,r of rank-2r symplectic instanton vector bundles on P3 with r 65 2 and second Chern class n 65 r, n 61 r(mod2). We give an explicit construction of an irreducible component In 17,r of this space for each such value of n and show that In 17,r has the expected dimension 4n(r + 1) 12 r(2r + 1). \ua9 2012 Versita Warsaw and Springer-Verlag Wien