# Tagged Questions

**2**

votes

**2**answers

206 views

### Etale covers of a hyperelliptic curve

Let $X$ be a hyperelliptic curve of genus at least two.
Let $Y\to X$ be a finite etale morphism with $Y$ connected.Then $Y$ is a smooth projective connected curve.
Is $Y$ hyperelliptic?
More ...

**3**

votes

**1**answer

137 views

### Higher Weierstrass points on curves of genus 3

So this question is directly related to a comment made by David Mumford in his
Lecture 1 given at U. Michigan in 1974 entitled: What is a curve and how explicitly can we describe them ?
Mumford ...

**1**

vote

**1**answer

212 views

### a question on the space of divisors on a curve

Let $X$ a complex curve and $x\in X$ a point.
We consider the space of effective divisors $D$ with fixed degree $d$, whic we know is isomorphic to $X^{d}/S_{d}$ where $S_{d}$ is the symmetric group.
...

**0**

votes

**1**answer

98 views

### Is the space of degree $d$ curves with marked smooth points dense inside the space of curves with marked points?

Let $\mathcal{D} \approx \mathbb{P}^{\delta_d} $ be the space of nonzero
homogeneous degree $d$ polynomials in three variables upto scaling, where
$\delta_d = \frac{d(d+3)}{2} $
(basically degree ...

**1**

vote

**1**answer

230 views

### $P^1$ minus k points

For $k\geq 3$, and $k$ arbitrary points $S=( z_1,\cdots,z_k ) \in \mathbb{P}^1$, we can write
$$ P^1 \setminus S \cong \mathbb{H}/G $$
where $\mathbb{H}$ is the upper-half plane and $G\subset ...

**8**

votes

**2**answers

407 views

### Proving that a generic variety with ample canonical bundle has no automorphisms

Let $X$ be a smooth projective connected variety over the complex numbers with ample canonical bundle. If $X$ is generic and $\dim X \leq1$, the automorphism group of $X$ is trivial, see for instance
...

**1**

vote

**1**answer

194 views

### Picard group of a K3 surface generated by a curve

In Lazarsfeld's article "Brill Noether Petri without degenerations" he mentions the fact that for any integer $g \geq 2$, one may find a K3 surface $X$ and a curve $C$ of genus $g$ on $X$ such that ...

**6**

votes

**1**answer

377 views

### If rational points are like entire curves, then what do algebraic points correspond to

I read somewhere that if $X$ is a projective variety of general type over a number field $K$, then rational points are an analogue of entire curves $\mathbf{C}\to X^{an}$ (with $X^{an}$ the ...

**1**

vote

**1**answer

171 views

### finite surjective morphism to the projective line

Let X a smooth projective curve over $\mathbb{C}$.
We fix $d$ distinct closed points $x_{1},\dots,x_{d}$.
Can we find a finite surjective morphism $\pi:X\rightarrow\mathbb{P}^{1}$
and local ...