Questions tagged [log-geometry]

Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory

17 questions
Filter by
Sorted by
Tagged with
79 views

algebraic de Rham cohomology of toric varieties (reference request)

I haven't been able to find anything workable yet, but I'm looking for a reference on the de Rham cohomology of toric varieties, where as many as possible of the following conditions are handled: ...
223 views

An unpublished note by Bloch-Kato on p-divisible groups and Dieudonné crystals

I wonder if anyone could find the following unpublished paper of Bloch-Kato: Spencer Bloch and Kazuya Kato, $p$-divisible groups and Dieudonné crystals, unpublished. A similar question is here ...
247 views

$p$-adic Kato--Nakayama space

Given a log scheme over $\mathbb{C}$ whose underlying scheme is locally of finite type, you can associate to it a ringed space called the Kato--Nakayama space. Is there a $p$-adic analogue of this ...
363 views

Properties of log smooth schemes

Let $k$ be a field and $M$ be sharp monoid (with no invertible element) consider the log point $\eta_M=(\operatorname{Spec}(k), M)$. Let $X$ be a fine saturated scheme over $\eta_M$ such that the ...
339 views

A log structure on the moduli space of curves

Let $M_{g, n}$ be the moduli space of curves of genus $g$ with $n$ marked points. Let $M_{g, \vec{n}}$ be the moduli space of marked curves with a choice of a (possibly zero) tangent vector at each ...
132 views

Locally toric resolutions of compactifications

Suppose $U$ is a smooth, open $n$-dimensional variety over $\mathbb{C}.$ Say $X, X'$ are two proper normal-crossings compactifications of $U$. Call a map $m: X'\to X$ a modification if it is an ...
324 views

An unpublished note by Spencer Bloch and Kazuya Kato

I am looking for an unpublished note by Spencer Bloch and Kazuya Kato, p-divisible groups and Dieudonné crystals. This note is always cited as Spencer Bloch and Kazuya Kato, p-divisible groups and ...
788 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 ...
465 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 ...
372 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 ...
426 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, ...
220 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 ...
1k 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 \$...
4k 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 ...
1k 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 ...