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Moscow Mathematical Journal, 2018, Volume 18, Number 1, Pages 117–148
DOI: https://doi.org/10.17323/1609-4514-2018-18-1-117-148
(Mi mmj665)
 

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
Full-text PDF Citations (7)
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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.
Bibliographic databases:
Document Type: Article
MSC: 14D20, 14J60
Language: English
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
Citation in format AMSBIB
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\by Marcos~Jardim, Dimitri~Markushevich, Alexander~S.~Tikhomirov
\paper New divisors in the boundary of the instanton moduli space
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 1
\pages 117--148
\mathnet{http://mi.mathnet.ru/mmj665}
\crossref{https://doi.org/10.17323/1609-4514-2018-18-1-117-148}
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  • This publication is cited in the following 7 articles:
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