pith. sign in

arxiv: 1501.00736 · v1 · pith:NVHYDO5Xnew · submitted 2015-01-05 · 🧮 math.AG

New divisors in the boundary of the instanton moduli space

classification 🧮 math.AG
keywords mathcalinstantonrankmathbbmoduliboundarycomponentsdimension
0
0 comments X
read the original abstract

Let ${\mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${\mathbb P}^3$. We know from several authors 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.