All Questions
8 questions
4
votes
1
answer
622
views
Is there a compact complex manifold with $b_1(X)=b_2(X)=b_3(X)=b_4(X)=0$?
As the title suggests, I have the following question:
Is there a compact complex manifold with $b_1(X)=b_2(X)=b_3(X)=b_4(X)=0$?
Clarification:
Denote by $b_k$ the $k$th Betti number of a compact ...
- 4,600
7
votes
1
answer
634
views
Hodge diamonds of complex threefolds
There is no closed complex curve or surface with $h^{1, 0}-h^{0, 1}=1$.
Now consider threefolds. Can this condition be satisfied?
Is Serre duality in fact the only restriction on the Hodge diamond?
- 19.3k
2
votes
1
answer
652
views
Complex manifold defined over $\mathbb{R}$
Let $M$ be a connected closed complex manifold with an antiholomorphic involution.
Must there be an atlas and a choice of a reference point in each chart such that the transition functions are ratios ...
- 53.3k
3
votes
0
answers
55
views
Infinitely many deformation equivalent Hodge diamonds II
Let $S$ be a connected smooth complex-analytic space. Let $\phi:X\to S$ be a proper holomorphic submersion with connected fibers. Can the fibers of $\phi$ have infinitely many distinct Hodge diamonds?
...
CommunityBot
- 1
2
votes
1
answer
128
views
Infinitely many deformation equivalent Hodge diamonds
Let $S$ be a connected open complex manifold. Let $\phi:X\to S$ be a proper holomorphic submersion with connected fibers. Can the fibers of $\phi$ have infinitely many distinct Hodge diamonds?
An ...
- 35.2k
3
votes
0
answers
98
views
Euler characteristic of an exhaustion of compacts of a surface
Let $X$ be an open (connected) Riemann surface of finite Euler characteristic. And $K_1 \subset \cdots K_n \subset$ be an sequence of closures of bounded open subsets with smooth boundary of $X.$
...
- 750
7
votes
1
answer
1k
views
Is a simply connected Ricci-flat Kaehler manifold a Calabi-Yau manifold?
Hi,
I have the following question: Let $(M,\omega, J)$ be a simply connected Kaehler manifold with Ricci-flat Kaehler metric. How can one show that $M$ is a Calabi-Yau manifold. By Calabi-Yau ...
- 3,540
3
votes
1
answer
831
views
Are Lefschetz thimbles holomorphic manifolds?
I have a Lefschetz thimble defined by the stable flow of the gradient a holomorphic function
toward a critical point (as defined e.g. in Witten arXiv:1001.2933 and F.Pham "Vanishing homologies and the ...
- 7,005