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Journal Article

New divisors in the boundary of the instanton moduli space

MPS-Authors
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Markushevich,  Dimitri
Max Planck Institute for Mathematics, Max Planck Society;

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Tikhomirov,  Alexander S.
Max Planck Institute for Mathematics, Max Planck Society;

Fulltext (public)

arXiv:1501.00736.pdf
(Preprint), 399KB

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Citation

Jardim, M., Markushevich, D., & Tikhomirov, A. S. (2018). New divisors in the boundary of the instanton moduli space. Moscow Mathematical Journal, 18(1), 117-148.


Cite as: http://hdl.handle.net/21.11116/0000-0003-FCB2-8
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.