# Questions tagged [kobayashi-hyperbolicity]

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10
questions

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66 views

### Holomorphic sectional curvature and Kobayashi hyperbolicity

Let $(M,g)$ be a compact Hermitian manifold. Let $\text{HSC}(g)$ denote the holomorphic sectional curvature of $g$. The implication $$\text{HSC}(g) < 0 \implies M \ \text{is Kobayashi hyperbolic}$$ ...

**10**

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265 views

### Examples of quasi-negative but not negative holomorphic sectional curvature

Let $(X,\omega)$ be a compact Kähler manifold and call $\operatorname{HSC}_{\omega}(x,[v])$ the holomorphic sectional curvature of the Chern connection of $\omega$ at the point $x\in X$ in the ...

**1**

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128 views

### Finding a metric on a topological space with prescribed isometry group

Let $X$ be a (sufficiently nice) topological space and let $\mathcal{F}$ be a group of homeomorphisms of $X$. Assume that $\mathcal{F}$ is also closed under point-wise convergence. I would like to ...

**13**

votes

**1**answer

736 views

### Examples of Brody hyperbolic affine varieties which are not Kobayashi hyperbolic

Let $X$ be a complex space.
We say that $X$ is Brody hyperbolic if there is no non-constant holomorphic map $f\colon\mathbb C\to X$.
We say that $X$ is Kobayashi hyperbolic if the Kobayashi pseudo-...

**9**

votes

**2**answers

796 views

### Finite etale atlas for Deligne-Mumford stacks

Let $X$ be a smooth finite type separated connected Deligne-Mumford stack over $\mathbb C$.
Does there exist a finite etale morphism $Y\to X$ with $Y$ a scheme?
What if $X$ is an algebraic space (i....

**9**

votes

**1**answer

312 views

### Non projective hyperbolic compact complex space

A famous conjecture by Kobayashi (perhaps slightly revisited subsequently) states that every compact hyperbolic Kähler manifold $X$ has ample canonical bundle.
This implies in particular that $X$ is ...

**3**

votes

**1**answer

216 views

### Which varieties of general type admit fibrations with non-general type fibres

Disclaimer. I don't know much about the things I'm asking. This is why my other question pencils on varieties of general type was a bit unclear. I believe the following question makes up for this.
...

**6**

votes

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445 views

### Jet differentials and hyperbolicity: possible mistake in the literature?

I was reading this note by Jingzhou Sun http://arxiv.org/abs/1109.1329
about Demailly's approach to hyperbolicity using jet differentials. The author seems to claim that there is a mistake in one of ...

**4**

votes

**3**answers

682 views

### Inequality of von Neumann for more than two contractions

Good morning,
I'm doing the Master 2 Practice at the University of Toulouse 3, France, on the spectral Nevanlinna-Pick interpolation, via operator theory. This problem leads to study the symmetrized ...

**11**

votes

**3**answers

2k views

### Why is a variety of general type hyperbolic?

I heard people mentioned this in one sentence, but don't see the reason.
Why a (smooth) variety of general type, i.e. an algebraic variety X with K_X big, is hyperbolic, i.e. has no non-constant map ...