All Questions
Tagged with algebraic-surfaces fibration
10 questions
3
votes
0
answers
221
views
Historical proof of Leschetz Hyperplane Theorem
I browse in Phillip Griffiths' Slides
on historical development of
Hodge-theory and these include a sketch of the original approach
with Lefschetz used to study complex surfaces in his famous
...
- 6,018
3
votes
1
answer
362
views
elliptic fibration over $\mathbb{P}^1$ with exactly two fibres with monodromy of unipotency rank 1
Despite the apparent simplicity of the following question I couldn't find the answer so far.
I am looking to construct an elliptic fibration $X \to \mathbb{P}^1$ with $X$ smooth, and exactly two ...
- 4,070
3
votes
0
answers
176
views
Elliptic fibration arising from a higher genus linear system
Let $H$ be a very ample linear system on a smooth compact complex surface $X$ whose Kodaira dimension is $\geq 0$. A general element of $H$ is smooth and has genus $\geq 2$.
Let $L\subset H$ be a ...
- 502
3
votes
1
answer
1k
views
Elliptic fibrations with few singular fibers
It is known that non-isotrivial fibrations of genus $g>0$ curves over the projective line have a bunch of singular fibers. There are at least three of them.
It is not difficult to prove that an ...
- 502
3
votes
3
answers
515
views
Does there exist a holomorphic fibration of genus two over $\mathbb{P}^{1}$ with $7$ nodal singularities?
This is a problem about the holomorphic fibration on a complex manifold.
Does there exist a holomorphic fibration of genus two over $\mathbb{CP}^{1}$ with 7 nodal singularities?
If you are aware of ...
- 31
3
votes
1
answer
555
views
Automorphisms of surfaces
Let $X$ be a projective surface with a morphism $f:X\rightarrow\mathbb{P}^1$. Assume that $f^{-1}(t)\cong\mathbb{P}^1$ for any $t\neq 0$ but $f^{-1}(0)$ is the union of two $\mathbb{P}^1$'s ...
user58018
6
votes
2
answers
2k
views
Isotrivial fibrations over $\mathbb P^1$
First of all I want to say that algebraic geometry is not "my field of research" so I apologize if the notation is not standard.
$S$ is a smooth complex projective surface with a fibration $...
- 297
10
votes
2
answers
839
views
Uniformization of Kodaira fibered surfaces
Consider a Kodaira fibration. i.e. a smooth non-isotrivial fibration $X\rightarrow C$ with $X$ a smooth complex surface and $C$ a smooth complex curve, such that both the genus of $C$ and genus of the ...
- 2,221
1
vote
0
answers
238
views
Classification of fibres in pencils of curves of genus two
For the case of characteristic positive, there exist some clasification of families of curves of genus two over a elliptic curve?.
- 11
3
votes
0
answers
367
views
Does there exist a non-isotrivial fibration of genus two over P^1 with only 3 singular fibres of general type surfaces?
We will work over the complex numbers C.
This question is based on Beauville's article :
there exist a non-isotrivial fibration of genus 2 over P^1 with only 3 singular fibres.
but not know for ...
- 31