Commuting matrices and the Hilbert scheme of points on affine spaces

Abstract

We give a linear algebraic and a monadic descriptions of the Hilbert scheme of points on the affine space of dimension $n$ which naturally extends Nakajima's representation of the Hilbert scheme of points on the plane. As an application of our ideas and recent results from the literature on commuting matrices, we show that the Hilbert scheme of $c$ points on $(\C^3)$ is irreducible for $c\le 10$.

Final version. 21 pages

References in corpus (4)

• Hilbert schemes of 8 points
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• ADHM construction of perverse instanton sheaves
• The ADHM Variety and Perverse Coherent Sheaves

Cited by in corpus (2)

• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• Moduli spaces of quasi-trivial sheaves