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Results tagged with moduli-spaces
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user 152042
Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
3
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Kodaira-Spencer map in logarithmic geometry
Can anyone provide a reference for the Kodaira-Spencer map in the logarithmic geometry setting?
- 494
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answers
170
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A silly doubt on Log structures
Let $X=\operatorname{Spec} A$ be an affine variety. Consider the log structure given by $\mathbb N\rightarrow A$ which sends $1\mapsto 0$. Also consider the log structure $\mathbb N^r \rightarrow A$ g …
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Semistable curves of genus $g\geq 2$ form an Artin algebraic stack in the etale topology?
I need the reference to a detailed proof the following fact.
Let $g\geq 2$ be an integer. Let $\mathcal M^{ss}_g: Sch\rightarrow Groupoids$ be the prestack which sends a scheme $T$ to the groupoid of …
- 494
0
votes
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On linear schemes
Let $X$ be a smooth projective curve and $T$ is any smooth variety. Let $E$ be a family of vector bundles over $X\times T$ which is flat over $T$. Then there exists a scheme $Y$ over $T$ such that for …
- 494
6
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154
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Logarithmic Darboux theorem
Let $X$ be a smooth complex analytic manifold and $D$ be a normal crossing divisor. Suppose that there is a complex analytic logarithmic symplectic structure on $X$.
Is there a Darboux like theorem th …
- 494
1
vote
0
answers
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On logarithmic schemes
I have two questions on logarithmic schemes
Can we explicitly construct a chart for any coherent logarithmic scheme? By definition of coherence it must have a chart but given a coherent sheaf of mon …
- 494
0
votes
0
answers
140
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Cartesian square in the category of Algebraic stacks
Suppose we have a commutative diagram of Artin stacks
$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\p …
- 494
2
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1
answer
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On the stack of semistable curves
This is a question related to
Semistable curves of genus $g\geq 2$ form an Artin algebraic stack in the etale topology?
Let $\mathcal C\rightarrow \mathcal M^{ss}_g$ be the universal curve over the A …
- 494
3
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answers
266
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On the normal crossing divisor of $\overline{\mathcal M}_g$
Let $g\geq 2$ be an integer. Let $\overline{\mathcal M}_g$ denote the DM stack of stable curves of genus $g$. It is well-known that the moduli stack is smooth and has a natural normal-crossing divisor …
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