The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
Year: 2026
Type: article
Abstract: For a fixed quasi-projective scheme X we introduce a self-dual analogue of Hilb d ( X ) which we call the Iarrobino scheme of X . It is a fine moduli space of zero-dimensional subschemes of X together with a self-dual filtration. It contains an open subset that parameterises oriented Gorenstein subschemes. We provide also self-dual analogues of the Quot scheme of points and of the stacks of coherent sheaves and finite algebras. We prove that the resulting analogues of Hilbert and Quot schemes are smooth for X a smooth curve. The Iarrobino scheme is a natural ambient space for enumerative invariants of algebras as introduced by Michałek. When X is an affine space, it also admits a commuting matrices description and related virtual structure.
Source: Advances in Mathematics
Author: Joachim Jelisiejew
Institution: University of Warsaw
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W4415993208