# Tagged Questions

**3**

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### Projective schemes with a fixed hyperplane section

Let $H$ be a hyperplane in $\mathbb P^n$, and $X \subseteq H$ be a subscheme. Let $CX \subseteq \mathbb P^n$ be the cone on $X$ from a point $p \notin H$.
Let $Hilb_{CX}$ be the Hilbert scheme whose ...

**2**

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189 views

### Is the universal closed subscheme reduced?

Let $G$ be a finite subgroup of $\text{SL}(2,\mathbb{C})$ and let $Y=\text{GHilb}(\mathbb{C}^2)$ be the minimal resolution of $X=\mathbb{C}^2/G$ where $\text{GHilb}(\mathbb{C}^2)$ is the Nakamura ...

**4**

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### “Reductive Groups and Hilbert Schemes” - Reference

Bezrukavnikov and Ginzburg have unpublished notes, 'Hilbert Schemes and Reductive Groups' (referenced here, for example): does anyone know what became of these notes? Did Bezrukavnikov-Ginzburg ...

**9**

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689 views

### Reference for combinatorics of cell decomposition of the Hilbert scheme of points in the plane

It is known from either Morse theory or Bialynicki-Birula decomposition that the fixed points of a ${\mathbb{C}}^*$ action on a smooth algebraic variety over $\mathbb{C}$ determine a cell ...

**7**

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920 views

### Reference request: is the punctual Hilbert scheme irreducible?

The punctual Hilbert scheme in dimension $d$ parameterizes ideals $I$ of codimension $n$ in $k[x_1,\dots, x_d]$ which are contained in some power of the ideal $(x_1,\dots, x_d)$. In other words, it is ...