**1**

vote

**2**answers

460 views

### Relative minimality for conic bundles

Due to difficulties in finding references I am not sure of what relative minimality is about for conic bundles. Suppose we're working on con. bun. over surfaces.
The definition is ok: the fiber over ...

**7**

votes

**1**answer

428 views

### Does a birational involution of C^n always have a fixed point?

The title describes completely the question.
For n=1 it is an easy exercise. For n=2 the statement is still true, and depends on the classification of birational involutions of P^2 (see e.g. ...

**10**

votes

**2**answers

656 views

### Rationality of GIT quotients

I recently worked through most of the proof of the rationality of the moduli of genus 3 curves, which seemed to have the following structure:
Every nonhyperelliptic genus 3 curve is a smooth plane ...

**3**

votes

**3**answers

293 views

### Nefness of $h-e$ in the blowup of $\mathbb{P}^n$

Let $S$ be the blow up of $\mathbb{P}^n$ in a point $P$. Let $h$ be the class of the pullback of an hyperplane of $\mathbb{P}^n$ and $e$ the class of the exceptional divisor. Why is the divisor ...

**2**

votes

**5**answers

601 views

### Reference for explicit calculation of blowups (of ideals) and strict transforms

Can one suggest some references where explicit calculations for blow up technique(along an ideal) and strict transformation is done in different examples?

**6**

votes

**3**answers

462 views

### Why is the Hodge class of \bar{M_g} big and nef?

Let pi: \bar{Mg,1} \to \bar{M_g} be natural projection of compactified moduli stacks of curves and let omega be the relative dualizing sheaf. Then the Hodge class \lambda of \bar{M_g} is the first ...