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9
votes
2answers
476 views

Minimal model which is necessarily singular

I was told during a summer school on the MMP a nice example (which I have also mentioned here on MO) that I'm not able to figure out anymore. The example (due, I think, to Miles Reid) is a smooth ...
1
vote
2answers
385 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
1answer
415 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
2answers
606 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
3answers
281 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 ...
1
vote
5answers
500 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
3answers
424 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 ...