All Questions
10 questions with no upvoted or accepted answers
13
votes
0
answers
743
views
Kähler-Ricci flow approach for Beauville-Bogomolov type decomposition?
Is there any Kähler Ricci flow method for solving structure theorems in Algebraic geometry
In fact If $X$ be a Calabi-Yau manifold then we can descend the Kähler Ricci flow to its finite etale ...
user21574
9
votes
0
answers
836
views
Is there a Calabi-Yau threefold with $h^{1,1}=1$ and $h^{1,2}=0$?
Is there a Calabi-Yau threefold with $h^{1,1}=1$ and $h^{1,2}=0$?
- 726
6
votes
0
answers
218
views
Can the base of an elliptically fibered Calabi-Yau threefold be an Enriques surface?
For this question, a Calabi-Yau manifold or variety of dimension $n$ is defined as a non-singular projective variety with trivial canonical bundle and $h^{i,0} = 0$ unless $i = 0$ or $i = n$.
If ...
- 515
5
votes
0
answers
300
views
Examples or references for this claim about elliptic Calabi-Yau threefolds
In this article (page 2) , the authors say:
"it is expected, based on known examples, that Calabi–Yau threefolds of large Picard
rank are always elliptically fibered, perhaps after flopping a ...
- 1,841
3
votes
0
answers
193
views
Smallest Hodge numbers of Calabi-Yau threefolds ever found
By a Calabi-Yau threefold, I mean a simply-connected smooth compact K"ahler threefold with trivial canonical class.
It has two independent Hodge numbers $h^{1,1}$ and $h^{1,2}$.
What is the ...
- 1,841
3
votes
0
answers
334
views
A question on fibered Calabi-Yau threefolds
Let $\phi:X\rightarrow \mathbb{P}^1$ be a fibered Calabi-Yau threefold with a general fiber $F$. The following are known
$\phi=\Phi_{mF}$ for some $m\in \mathbb{N}$, where $\Phi_D$ stands for the map ...
- 31
2
votes
0
answers
129
views
Hodge coniveaux of Calabi-Yau manifolds
Let $X$ be a strict compact Calabi-Yau manifold of dimension $n$. By this, I mean that $X$ is a simply connected projective manifold whose holomorphic forms are generated by a nowhere zero top degree ...
- 279
2
votes
0
answers
201
views
Betti numbers of threefolds with trivial canonical class
I am interested in a simply-connected compact complex manifold $M$ of dimension three with trivial canonical class.
Note that if it is K"ahler, then it is a Calabi-Yau threefold.
Its independent ...
- 1,841
2
votes
0
answers
151
views
Minimal Betti numbers of simply-connected threefolds with trivial canonical class
By a threefold, I mean a compact complex manifold of dimension three.
For a simply-connected threefold with trivial canonical class, its Betti numbers satisfy:
$$b_2 \ge 0, b_3 \ge 2.$$
I am wondering ...
- 1,841
2
votes
0
answers
482
views
What is a moduli space of Calabi-Yau threefolds?
A Calabi-Yau threefold is a compact Kahler threefold which is simply connected and has trivial canonical bundle.
So my question is as in the title. What is the moduli space of such objects? I'm ...
- 936