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JOURNALS // Moscow Mathematical Journal // Archive

Mosc. Math. J., 2018 Volume 18, Number 1, Pages 117–148 (Mi mmj665)

This article is cited in 7 papers

New divisors in the boundary of the instanton moduli space

Marcos Jardima, Dimitri Markushevichb, Alexander S. Tikhomirovc

a IMECC — UNICAMP, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, 13083-970 Campinas-SP, Brazil
b Mathématiques – bât. M2, Université Lille 1, F-59655 Villeneuve d'Ascq Cedex, France
c Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva Street, 119048 Moscow, Russia

Abstract: Let $\mathcal I(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on $\mathbb P^3$. It is known that $\mathcal I(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since every rank $2$ instanton bundle on $\mathbb P^3$ is stable, we may regard $\mathcal I(n)$ as an open subset of the projective Gieseker–Maruyama moduli scheme $\mathcal M(n)$ of rank $2$ semistable torsion free sheaves $F$ on $\mathbb P^3$ with Chern classes $c_1=c_3=0$ and $c_2=n$, and consider the closure $\overline{\mathcal I(n)}$ of $\mathcal I(n)$ in $\mathcal M(n)$.
We construct some of the irreducible components of dimension $8n-4$ of the boundary $\partial\mathcal I(n):=\overline{\mathcal I(n)}\setminus\mathcal I(n)$. These components generically lie in the smooth locus of $\mathcal M(n)$ and consist of rank $2$ torsion free instanton sheaves with singularities along rational curves.

Key words and phrases: sheaves on projective spaces, instantons, moduli spaces of sheaves, stable sheaves.

MSC: 14D20, 14J60

Language: English

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



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