All Questions
Tagged with enumerative-geometry projective-geometry
7 questions
11
votes
2
answers
557
views
Hypersurface of singular plane cubics
In the projective space $\mathbb{P}^9 = \mathbb{P}(\mathbb{C}[x,y,z]_3)$, parametrizing plane cubics, consider the hypersurface $X\subset\mathbb{P}^9$ whose points corresponds to singular cubics. The ...
- 8,998
2
votes
1
answer
210
views
Configuration of points on a plane curve
Let $C\subset\mathbb{P}^2$ be a smooth plane curve of degree six. On $C$ there are $21$ points given as the intersection points of two lines choosen among a set of seven lines. More precisely there ...
user61586
2
votes
0
answers
179
views
Quadrics tangent to lines
I think that the following must be a basic question in enumerative geometry.
Take a line $L\subset\mathbb{P}^3$. The quadric surfaces in $\mathbb{P}^3$ that are tangent to $L$ are parametrized by a ...
user114666
7
votes
1
answer
293
views
Largest number of points one can pick in finite projective space without getting three on a line
Consider the projectivization $\mathbb P\mathbb F_p^n$ of $\mathbb F_p^n$. How large a set $B \subseteq \mathbb P \mathbb F_p^n$ can I pick so that no three points of $B$ lie on the same line?
- 615
2
votes
1
answer
124
views
Piercing of subspaces in a projective space?
The "piercing subspace" problem may be stated as follows:
There are given several subspaces in a projective space, rather non-intersecting.
Find an additional subspace of a prescribed dimension that ...
2
votes
1
answer
401
views
degree 7 rational curves through ten points in P4
This is a very classical flavoured question, and probabaly it is not difficult. I would like to know the shape of the space of rational degree 7 curves in $P^4$ that pass through 10 fixed points. By "...
- 3,779
3
votes
1
answer
707
views
Counting curves of degree 4 in $\mathbb{P}^{3}$
Let $p_1,...,p_8\in\mathbb{P}^{3}$ be points in linear general position. Then there exists a unique elliptic curve $C$ of degree $4$ passing through $p_1,...,p_8$. I am interested in what happens for ...
- 8,998