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arXiv · 2306.11521

Fixed point distribution on Hilbert scheme of points

Gergely Bérczi·Jonas M. Svendsen
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Abstract

Let $\mathbf{k}$ be a closed field of characteristic zero. We prove that all monomial ideals sit in the curvilinear component of the Hilbert scheme of points of the affine space $\mathbb{A}_{\mathbf{k}}^n$, answering a long-standing question about the distribution of torus-fixed points among punctual components. This result confirms that the punctual Hilbert scheme is connected, a property previously established only for the full Hilbert scheme in 1966 by Hartshorne.

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Gergely Bérczi, Jonas M. Svendsen. 2023-06-20. Fixed point distribution on Hilbert scheme of points. https://arxiv.org/abs/2306.11521

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