**8**

votes

**1**answer

294 views

### When is a map from a logarithmic tangent bundle to a normal bundle surjective?

Suppose that $X$ is an algebraic variety with divisor $D$ such that the logarithmic tangent bundle $\mathcal{T}_X(-\log D)$ is locally free. Suppose moreover that $\iota\colon Y\to X$ is a regular ...

**5**

votes

**0**answers

190 views

### Semistable reduction and log structures

I have been reading Hyodo-Kato's paper on log-crystalline cohomology, and there is one statement there that has been troubling me.
To explain this, suppose we have a perfect field $k$ of ...

**1**

vote

**1**answer

253 views

### trivialities on log-structures

I would like to understand some trivialities about log-structures. Given a log-scheme $(X,M_X)$ the log-structure $M_X$ is defined via push-out. Are there stupid examples in which this push-out is ...

**2**

votes

**1**answer

347 views

### Minimal semistable model for K3-surfaces.

I wonder if a semistalbe K3 surface over a $p$-adic field has a minimal semistable model. I guess yes but I do not find any reference.
Also, if we have a semistable K3 surface with a log structure, ...

**1**

vote

**0**answers

180 views

### Moduli Space of an Algebraic K3 surface with singularities.

Suppose that $X$ is an algebraic K3 surface (say polarized). If the singular divisor of $X$ is normal crossing... Do we have a moduli space parametrizing such $K3$ surfaces? If yes do we have a ...

**5**

votes

**3**answers

890 views

### relation between toric geometry and log geometry

Hello,
I'm trying to understand the relation between the points of view of
log geometry (monoids) and toric geometry (fans).
Suppose that $k$ is a field and $P$ is a finitely generated monoid.
Then $...

**11**

votes

**4**answers

3k views

### References for logarithmic geometry

Hi everyone,
I'm looking for a systematical introduction to (or treatment of) logarithmic structures on schemes. I am reading Kato's article ("Logarithmic structures of Fontaine-Illusie") at the ...

**4**

votes

**2**answers

600 views

### What are Log Stacks

So, I've been running in both stacky circles and logarithmic circles and I've been wondering: is there a definition of log stack that is "useful"? I can imagine two such definitions:
1) A log stack ...

**11**

votes

**0**answers

672 views

### Kato's log motives

What are they and what are their intended uses? Does anyone have notes/slides of this talk?
I am curious about "log motives" because there seems to exist a "log motivic yoga" among experts in ...

**7**

votes

**2**answers

673 views

### Logarithmic structures on moduli of elliptic curves over Z

I've heard it stated that if you take the moduli of elliptic curves with some level structure imposed (as a moduli scheme over Spec(Z)), there is a logarithmic structure that you can impose at the ...