The singularities of the principal component of the Hilbert scheme of points
Kyungyong Lee
TL;DR
This paper investigates the geometric properties of the principal component of the Hilbert scheme of 9 points in 8-dimensional complex space, revealing it is not Cohen-Macaulay, which impacts understanding of its singularities.
Contribution
It demonstrates that the principal component of the Hilbert scheme of 9 points in C^8 is not Cohen-Macaulay, providing new insights into its singular structure.
Findings
The principal component of the Hilbert scheme of 9 points in C^8 is not Cohen-Macaulay.
This result highlights complex singularities in high-dimensional Hilbert schemes.
The study advances understanding of the geometric and algebraic properties of Hilbert schemes.
Abstract
We show that the principal component of the Hilbert scheme of 9 points in C^8 is not Cohen-Macaulay.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic and Geometric Analysis · Holomorphic and Operator Theory