# Tagged Questions

**3**

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155 views

### How to induce infinitesimal deformations on curves

Let $C_1, C_2$ be two projective curves (a scheme of pure dimension $1$) in $\mathbb{P}^3$.
The Hilbert scheme of curves contains informations of deformations of curves in $\mathbb{P}^3$. The question ...

**3**

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138 views

### 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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181 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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192 views

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Bezrukavnikov and Ginzburg have unpublished notes, 'Hilbert Schemes and Reductive Groups' (referenced here, for example): does anyone know what became of these notes?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

votes

**3**answers

662 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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**3**answers

879 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 ...