All Questions
7 questions
13
votes
1
answer
863
views
Generalization of the rigidity lemma in birational geometry
Let $X,Y,Z$ be projective varieties, and let $f:X\rightarrow Y$, $g:X\rightarrow Z$ be dominant morphisms. Assume that all the fibers of $g$ have the same dimension and are connected.
If there exists ...
user75933
4
votes
3
answers
450
views
Existence of a morphism between two toric varieties
Does there exist a morphism between the blow-up of $\mathbb{P}^3$ in four general points and $\mathbb{P}^1\times\mathbb{P}^1$? If not why?
user68440
2
votes
1
answer
186
views
Decomposition of a morphism with positive dimensional fibers
It is well known that any birational morphism between projective varieties is a sequence of blow ups. Suppose now that I have a morphism $f:X \to Y$ with positive dimensional fibers, that is a ...
- 3,779
2
votes
0
answers
309
views
Extension of a rational section of a projective bundle
Let us assume that we work over the complex field and let $X$ be a smooth projective variety and $\pi: P \to X$ a projective bundle (i.e. a fibration in projective spaces of constant dimension). Let $...
- 3,779
1
vote
2
answers
404
views
Fibrations on blow-ups of $\mathbb{P}^2$
Let $X_n = Bl_{p_1,...,p_n}\mathbb{P}^2$ be the blow-up of $\mathbb{P}^2$ in $n$ general points $p_1,...,p_n\in\mathbb{P}^2$.
Let $f_i:\mathbb{P}^{2}\dashrightarrow\mathbb{P}^1$ be the linear ...
user68440
1
vote
0
answers
168
views
Cohomology of a stratified projective bundle
Let $S$ be a smooth algebraic variety, and suppose $X\to S$ is a smooth morphism of schemes such that the geometric fibers are all projective spaces. Let us suppose that the dimension of the fibers is ...
- 3,779
0
votes
1
answer
323
views
Morphisms contracting a family of curves
Let $f:X\rightarrow Y$ be a morphism of normal projective varieties. Let $S\subseteq X$ be a surface admitting a morphism $g:S\rightarrow C$ to a curve $C$ such that any fiber of $g$ is a curve.
...
user58018