The kobayashi-hyperbolicity tag has no wiki summary.

**9**

votes

**0**answers

198 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 ...

**8**

votes

**2**answers

445 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 ...

**8**

votes

**1**answer

163 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

128 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.
...

**5**

votes

**0**answers

358 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

460 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 ...

**9**

votes

**3**answers

837 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 ...