• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

New divisors in the boundary of the instanton moduli space

Moscow Mathematical Journal. 2018. Vol. 18. No. 1. P. 117-148.
Jardim M., Markushevich D., Tikhomirov A. S.

Abstract. Let I(n) denote the moduli space of rank 2 instanton bundles of charge n on P3 . It is known that I(n) is an irreducible, nonsingular and affine variety of dimension 8n − 3. Since every rank 2 instanton bundle on P3 is stable, we may regard I(n) as an open subset of the projective Gieseker–Maruyama moduli scheme M(n) of rank 2 semistable torsion free sheaves F on P3 with Chern classes c1 = c3 = 0 and c2 = n, and consider the closure \overline{I(n)} of I(n) in M(n). We construct some of the irreducible components of dimension 8n − 4 of the boundary ∂I(n) := \overline{I(n)} \ I(n). These components generically lie in the smooth locus of M(n) and consist of rank 2 torsion free instanton sheaves with singularities along rational curves.