English

New divisors in the boundary of the instanton moduli space

Algebraic Geometry 2018-04-17 v1

Abstract

Let I(n){\mathcal I}(n) denote the moduli space of rank 22 instanton bundles of charge nn on P3{\mathbb P}^3. We know from several authors that I(n){\mathcal I}(n) is an irreducible, nonsingular and affine variety of dimension 8n38n-3. Since every rank 22 instanton bundle on P3{\mathbb P}^3 is stable, we may regard I(n){\mathcal I}(n) as an open subset of the projective Gieseker--Maruyama moduli scheme M(n){\mathcal M}(n) of rank 22 semistable torsion free sheaves FF on P3{\mathbb P}^3 with Chern classes c1=c3=0c_1=c_3=0 and c2=nc_2=n, and consider the closure I(n)\overline{{\mathcal I}(n)} of I(n){\mathcal I}(n) in M(n){\mathcal M}(n). We construct some of the irreducible components of dimension 8n48n-4 of the boundary I(n):=I(n)I(n)\partial{\mathcal I}(n):=\overline{{\mathcal I}(n)}\setminus{\mathcal I}(n). These components generically lie in the smooth locus of M(n){\mathcal M}(n) and consist of rank 22 torsion free instanton sheaves with singularities along rational curves.

Keywords

Cite

@article{arxiv.1501.00736,
  title  = {New divisors in the boundary of the instanton moduli space},
  author = {Marcos Jardim and Dimitri Markushevich and Alexander S. Tikhomirov},
  journal= {arXiv preprint arXiv:1501.00736},
  year   = {2018}
}

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30 pages