# Tagged Questions

**2**

votes

**1**answer

280 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 ...

**0**

votes

**1**answer

136 views

### Curve of degree $d$ through $2d+1$ points in $\mathbb P^3$

It is known that a Hilbert scheme of degree $d$ curves in $\mathbb P^3$ can have dimension more than $4d$. But, does it imply that for some types of curves there are such a curve through any, say, ...

**2**

votes

**1**answer

148 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 ...

**5**

votes

**1**answer

396 views

### Nagata's conjecture in positive characteristic

For a $\mathbb C P^2$ is known a result: if through the generic points $p_1,p_2,\dots p_n$ with multiplicities $m_1,m_2\dots, m_n$ correspondingly a degree $d$ irreducible reduced curve passes then ...

**5**

votes

**0**answers

159 views

### Counting plane curves over various fields

Fix two integers $d$ and $g$. The number of genus $g$ and degree $d$ curves passing through $3d+g-1$ generic points on the complex projective plane is finite and doesn't depend on the choice of ...

**1**

vote

**1**answer

219 views

### Riemann-Roch and dim of deformation space.

Let's consider curve $C\subset \mathbb P^n$ of degree $d$ and genus $g$. We want to calculate dimension of deformation space of $C$, i.e. $h^0(C,L)$ where $L$ is the normal bundle.
We can decompose ...

**5**

votes

**2**answers

1k views

### Nagata's conjecture, Seshadri constant

What is it known now about Nagata's conjecture and Seshadri constant (http://en.wikipedia.org/wiki/Nagata%27s_conjecture_on_curves and http://en.wikipedia.org/wiki/Seshadri_constant) for toric ...

**6**

votes

**2**answers

371 views

### How do the number of plane curves over a finite field of a fixed genus increase with the degree?

Let $k$ be a finite field. We define $N(d,g)$ to be the number of plane curves $f(x,y)$ defined over $k$ of degree $d$ with (geometric) genus $g$. If $D(d) := (d-1)(d-2)/2$ (the maximum possible ...