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This article is cited in 7 scientific papers (total 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.
Citation:
Marcos Jardim, Dimitri Markushevich, Alexander S. Tikhomirov, “New divisors in the boundary of the instanton moduli space”, Mosc. Math. J., 18:1 (2018), 117–148
Linking options:
https://www.mathnet.ru/eng/mmj665 https://www.mathnet.ru/eng/mmj/v18/i1/p117
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Abstract page: | 251 | References: | 43 |
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