Moscow Mathematical Journal

Volume 18, Issue 1, January–March 2018 pp. 117–148.

New Divisors in the Boundary of the Instanton Moduli Space

Authors: Marcos Jardim (1), Dimitri Markushevich (2), and Alexander S. Tikhomirov (3)
Author institution:(1) IMECC – UNICAMP, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, 13083-970 Campinas-SP, Brazil
(2) Mathématiques – bât. M2, Université Lille 1, F-59655 Villeneuve d'Ascq Cedex, France
(3) Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva Street, 119048 Moscow, Russia

Summary:

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.

2010 Math. Subj. Class. 14D20, 14J60.

Keywords: Sheaves on projective spaces, instantons, moduli spaces of sheaves, stable sheaves.

Contents Full-Text PDF