All Questions
Tagged with hilbert-schemes algebraic-curves
10 questions with no upvoted or accepted answers
5
votes
0
answers
245
views
Is the Chow scheme of 1-cycles the space of Cohen-Macaulay curves?
Let $C\subset X$ be a smooth irreducible curve of genus $g$, embedded in a smooth projective 3-fold $X$. So its homology class $\beta=[C]\in H_2(X)$ is an irreducible class. I want to compare two ...
- 1,534
3
votes
0
answers
226
views
When are Hilbert schemes connected by piecewise smooth curves?
Are there examples of Hilbert scheme $H$ of curves in $\mathbb{P}^3$ such that there exists an irreducible component $L$ of $H$ such that for any two points in $L$, there exist smooth projective ...
- 833
2
votes
0
answers
250
views
Smoothness of Hilbert scheme of rational normal curves
I'm trying to solve Exercise 1.26 from the book "Moduli of Curves"
by Harris and Morrison on page 14:
Exercise (1.26) Determine the normal bundle to the rational normal
curve $C \subset \...
- 6,028
2
votes
0
answers
153
views
An analogue of Brill-Noether for hypersurfaces?
Let $d,g,r$ be natural numbers such that $d \geq 1$, $g \geq 2$, $r \geq 3$. Denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme classifying subschemes of $\mathbb{P}^r$ with Hilbert polynomial $P(x) = ...
- 1,981
2
votes
0
answers
104
views
A basic question on complete intersection liaisons of curves
I am a beginner in the Linkage theory and would like to clarify certain points I am not sure of.
Let $P$ be the Hilbert polynomial of a curve in $\mathbb{P}^3$. Let $L$ be an irreducible component of ...
- 73
2
votes
0
answers
357
views
Deformation of complete intersection curves
Let $\mathcal{X} \to B$ be a family of smooth surfaces in $\mathbb{P}^3$. Let $\mathcal{C} \to B$ be a family of curves in $\mathbb{P}^3$. Assume that for all $b \in B$, the fiber $\mathcal{C}_b$ is ...
- 833
1
vote
0
answers
84
views
Relation between quot scheme of birational curve
I am very new to algebraic geometry. Currently reading about Hilbert and quot scheme. I want to know more about the structure and properties of Hilbert and quot schemes over curves. My question is the ...
- 613
1
vote
0
answers
141
views
Constructing embedded families of curves with general moduli
Is there a known way to construct flat families of smooth curves $\mathcal{C}/\mathcal{B}$ which are fiberwise embedded in a family of projective varieties $\mathcal{X}/\mathcal{B}$ and which have ...
- 1,981
1
vote
0
answers
124
views
Set of smooth curves on the Hilbert scheme is open. H
Let $H = Hilb_{d,g,r}$ be the Hilbert scheme of genus $g$ curves of degree $d$ in proyective space $\mathbb{P}^r$, over an algebraically closed field $k$.
Is it true that the set of points of $H$ ...
- 27
1
vote
0
answers
125
views
Obstruction to Gorenstein Liaisons of space curves
Let $P_1,P$ be Hilbert polynomials of curves in $\mathbb{P}^3$. Denote by $H_{P_1,P}$ the flag Hilbert scheme parametrizing pairs $(C_1 \subset C)$ where $C_1, C$ are of Hilbert polynomials $P_1$ and $...
- 503