# 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 ℙ^{3}. It is known that ℐ(*n*) is an irreducible, nonsingular and affine variety of dimension 8*n*−3. Since every rank 2 instanton
bundle on ℙ^{3} 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 ℙ^{3} with Chern classes *c*_{1} = *c*_{3} = 0 and *c*_{2} = *n*,
and consider the closure \overline{ℐ(*n*)} of ℐ(*n*) in ℳ(*n*).

We construct some of the irreducible components of dimension 8*n*−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.

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