NEW DIVISORS IN THE BOUNDARY OF THE INSTANTON MODULI SPACE

作者：Jardim Marcos^*; Markushevich Dimitri; Tikhomirov Alexander S.

来源：Moscow Mathematical Journal, 2018, 18(1): 117-148.

DOI：10.17323/1609-4514-2018-18-1-117-148

• Sheaves on projective spaces
• instantons
• moduli spaces of sheaves
• stable sheaves

Let I(n) denote the moduli space of rank 2 instanton bundles of charge n on P-3. It is known that I(n) is an irreducible, nonsingular and affine variety of dimension 8n - 3. Since every rank 2 instanton bundle on P-3 is stable, we may regard 1(n) as an open subset of the projective Gieseker-Maruyama moduli scheme M (n) of rank 2 semistable torsion free sheaves F on P-3 with Chern classes c(1) = c(3) = 0 and c(2) = n, and consider the closure <(I(n))over bar> of I(n) in M(n).
We construct some of the irreducible components of dimension 8n-4 of the boundary partial derivative I(n) := <(I(n))over bar>\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.

• 出版日期2018-3