Questions tagged [hilbert-schemes]
The hilbert-schemes tag has no usage guidance.
105 questions with no upvoted or accepted answers
0
votes
0
answers
146
views
Limit of a sequence of smooth varieties in Hilbert scheme
Let $\{Z_i\}_{i=1}^\infty$ be a sequence of smooth irreducible $k$-dimensional submanifolds of $\mathbb{C}\mathbb{P}^n$ which converges to a closed subscheme $Z$ in the sense of the Hilbert scheme of $...
- 21.8k
0
votes
0
answers
160
views
hilbert quot stacks vs schemes
What is the calculation that shows that the Hilbert or Quot functors could be represented by schemes (under various noetherian, (quasi) projectivity hypotheses), and do not require extending to the ...
- 785
0
votes
0
answers
214
views
Deformation of rational points in a family
Let $\mathcal{X} \to B$ be a family of smooth projective varieties over a field $K$ (possibly finite). Assume that each fiber $\mathcal{X}_b$ of the family has a $K$-rational point. Fix a pair $(p,\...
- 2,032
0
votes
0
answers
401
views
Normal sheaf of non-reduced locally complete intersection space curves
Let $C$ be a non-reduced locally complete intersection curve on a smooth degree $d$ surface in $\mathbb{P}^3$ (for example a non-reduced Cartier divisor). For simplicity we can assume that $d>deg(C)...
- 1,040
0
votes
0
answers
164
views
Maximum number of generators of a curve in $\mathbb{P}^3$
Let $H_{d,g}$ denote the Hilbert scheme of curves of degree $d$ and genus $g$ locally of complete intersection in $\mathbb{P}^3$. Given a curve $C \in H_{d,g}$, denote by $S(C)$ a minimal set of ...
- 1,040