Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with moduli-spaces
Search options not deleted
user 121
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.
2
votes
More questions about log structures
If you're compactifying a moduli space by choosing degenerations, you typically assign the trivial log structure to the uncompactified space. Given a point $x$, the size of the characteristic $M_{X,x …
2
votes
What is an example of a function on M_g?
For g=2, you can make functions using the fact that genus 2 curves are hyperelliptic. There is a finite map from an open subset of (P^1)^3 to M_2 given by taking the 2-fold cover of P^1 branched at 0 …
- 45.7k
1
vote
What is the difference between the moduli space of curves and the moduli space of orbi-curves?
If you want to express the stack of hyperelliptic curves in terms of a genus zero moduli problem, you have a few options:
You may view a hyperelliptic curve equipped with its hyperelliptic involutio …
- 45.7k
14
votes
Help motivating log-structures
Sometimes, it is not easy to choose a compactification of a moduli space, especially if the objects being parametrized are complicated - one may find that a choice of degenerate structure is too permi …
4
votes
Accepted
A question about moduli spaces over $\mathbb{Z}$
In general, maps over $W$ from $W$ to $X \times W$ are the same as maps from $W$ to $X$, by the universal property of products. Here, $W = \operatorname{Spec} \mathbb{C}$. I think one possible reaso …
- 45.7k
7
votes
Accepted
Kodaira-Spencer Theory and moduli of curves
By standard deformation theory (see e.g., Hartshorne III Ex 4.10, but there are probably better references), the tangent sheaf of $\mathscr{M}_g$ is $R^1\pi_{\ast}(\mathscr{C}, T_{\mathscr{C}/\mathscr …
- 45.7k
5
votes
Dualizing sheaf on singular curves
The dualizing sheaf looks like the sheaf of 1-forms, with logarithmic singularities at nodes (of the form f(z)dz/z, f regular at 0) such that the residues on each component of a node add to zero. The …
- 45.7k
7
votes
moduli interpretations for modular curves
For your first question, I can give an application close to my own field. Perhaps a more Langlands-ish person can say something interesting about applications to modularity of Galois representations. …
- 45.7k
16
votes
Accepted
Special fiber of $X(p)$ in characteristic $p$
A bit of mastication of Katz-Mazur Theorem 13.7.6 and the surrounding text seems to yield the following description of the special fiber of $Y(p)$:
It is fundamentally $p+1$ copies of $\mathbb{P}^1$ …
- 45.7k
8
votes
Accepted
Details for the action of the braid group B_3 on modular forms
You can think of the space of positively oriented covolume-one bases of $\mathbb{R}^2$ as a torsor under $SL_2(\mathbb{R})$, i.e., it is a manifold with a simply transitive action of the group. If yo …
- 45.7k
1
vote
Choosing tau for elliptic curves over the rational numbers with prescribed ramification data
I am having difficulty making sense of question 1. If you already know $f$, then you have $E$, which gives you an $SL_2(\mathbb{Z})$-orbit of values of $\tau$. This seems to be the best you can do.
…
- 45.7k
5
votes
A log structure on the moduli space of curves
As Piotr Achinger suggested in a comment, your log moduli space is the direct product of $M_{g,n}$ with the log point $\operatorname{Spec}(\mathbb{N}^n \to \mathbb{C})$ given by the monoid map $(x_1,\ …
- 45.7k
12
votes
0
answers
446
views
Where is the representability of the moduli of curves with framed points proved?
There is a variant of the Knudsen-Mumford moduli problem $\mathcal{M}_{g,n}$ of pointed curves, where one endows the $n$ marked points with non-zero tangent vectors. It shows up in the theory of vert …
- 45.7k
6
votes
Accepted
Modular curve parametrizing two cyclic subgroups of an elliptic curve
$Y_0(M,N)$ can be reinterpreted as the moduli space of diagrams $E_1 \to E \leftarrow E_2$ of elliptic curves, where the arrows are cyclic isogenies of degree $M$ and $N$. From this viewpoint, it is …
- 45.7k