# Tagged Questions

**2**

votes

**1**answer

172 views

### Questions on the Hodge Dual of the Kähler Class

Let $M$ be a compact complex surface, i.e., a complex manifold with complex dimension two. Also, let us denote its Kähler metric by $g$ and its Kähler form by $K$. Let us denote the Kähler class by ...

**3**

votes

**0**answers

222 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 ...

**16**

votes

**2**answers

579 views

### Moishezon manifolds with vanishing first Chern class

Suppose $M$ is a Moishezon manifold with $c_1(M)=0$ in $H^2(M,\mathbb{R})$. Does it follow that $K_M$ is torsion in $\mathrm{Pic}(M)$?
This is true whenever $M$ is Kähler (and therefore ...

**8**

votes

**1**answer

627 views

### Calabi-Yau fiber space without singular fibers implies finite quotient of product?

While reading this paper of Kollár, the following question came up. If $f:X\to Y$ is a fiber space (i.e. surjective holomorphic map with connected fibers) with $X,Y$ smooth projective ...

**3**

votes

**2**answers

406 views

### calabi conjecture on compact manifolds

hi,
is the calabi conjencture formulated for compact manifolds with boundary ? or only for those without boundary ? excuse me if the question is too trivial but in my literature it isn't mentioned ...

**10**

votes

**1**answer

1k views

### Theorem of Bryant in higher dimensions

hallo,
i have the following question. i read about Bryant's theorem which sais that: any real-analytic 3-dimensional Riemannian manifold $(Y,g)$ with real-analytic metric $g$ can be isometrically ...

**2**

votes

**2**answers

256 views

### Condition on the canonical divisor for Yau Inequality - effective or ample?

Let $X$ be a complex, projective, nonsingular variety. We also understand it as a Kähler Manifold. My question now is, when people say $c_1(X) < 0$, what exactly do they mean? Let me elaborate. In ...

**16**

votes

**1**answer

753 views

### Rational or elliptic curves on Calabi-Yau threefolds

Let $X$ be a Calabi-Yau threefold. From a complex analytic point of view, it is widely believed that it should not be Kobayashi hyperbolic, that is it should always admit some non-constant entire map ...

**1**

vote

**1**answer

454 views

### is complex moduli space of a Calabi - Yau Kahler

The complex moduli space of a Calabi-Yau manifold is a complex manifold (BTT). Is it also Kahler ?

**6**

votes

**3**answers

642 views

### what is large compex structure limit of CY moduli space

What is the Large Complex Structure limit(LCL) of complex moduli space of a Calabi-Yau 3-fold and why do we need to consider LCL in Mirror symmetry.

**2**

votes

**1**answer

541 views

### Are there non-supersymmetric and/or non-Calabi-Yau topological sigma models?

I am reading some aspects of Mirror Symmetry and in mirror symmetry the $N=2$ SCFT on a Calabi Yau Manifold can be divided into two sectors each of which is a topological sigma model, A-Model and ...

**9**

votes

**3**answers

2k views

### Calabi - Yau Manifolds

I just started reading about Calabi-Yau manifolds and most of the sources I came across defined Calabi-Yau manifold in a different way. I can see that some of them are just same and I can derive one ...