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Results tagged with moduli-spaces
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user 4096
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.
14
votes
0
answers
2k
views
conformal blocks for beginners
I have given now a couple of talks that involve conformal blocks bundles on the moduli stack $\overline{\mathcal{M}}_{g,n}$, in front of a public of algebraic geometers but not specialists of the fiel …
- 3,779
9
votes
2
answers
835
views
$Pic$ of the stack of elliptic curves vs. $Pic$ of the coarse space
There's a natural map $f:\overline{\mathcal{M}}_{1,1}\to \overline{M}_{1,1}\cong \mathbb{P}^1$ from the stack of elliptic curves to the coarse space. Both spaces have $Pic=\mathbb{Z}$ hence $f^*:\math …
- 3,779
7
votes
1
answer
538
views
Picard group of $\mathcal{M}_{0,n}$
Let $\mathcal{M}_{0,n}$ be the complement of the boundary of the Mumford-Knudsen compactification of the moduli space of genus zero, n-pointed curves.
Is $Pic(\mathcal{M}_{0,n})$ trivial?
- 3,779
7
votes
1
answer
459
views
kapranov's realization of $\overline{M}_{0,n}$ over other fields
Kapranov gave a very nice desciption, over $\mathbb{C}$ of the moduli space of stable pointed rational curves $\overline{M}_{0,n}$ as a series of blow-ups of $P^{n-3}$. Does this, or a similar result, …
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6
votes
Do mapping classes have gonality?
it seems that your question about the possible surjectivity of the map
$$\pi_1(T_g) \to \pi_1(M_g)$$
has been recently answered positively in http://arxiv.org/abs/1403.7399 (see the very first page …
- 3,779
6
votes
3
answers
819
views
examples of moduli functors for which coarse moduli space does not exists
Well, the title almost says it all. I would like to list as many examples as possible of moduli functors, for which a coarse moduli space does not exist (and maybe explain why). So, examples such as $ …
- 3,779
5
votes
2
answers
562
views
density of singular K3 surfaces
By singular K3 I mean a smooth complex K3 with Néron-Severi rank equal to 20.
Are singular K3 surfaces dense in the moduli space of polarized K3 surfaces?
- 3,779
4
votes
0
answers
298
views
Cohomology and deformations of moduli of vector bundles
I believe that the following is well-known, but I cannot find a reference
in the literature...
Let $X$ be a smooth variety (in our case $X = M^s(r)$ coarse moduli space of stable rank $r$ vector bund …
- 3,779
4
votes
0
answers
481
views
Stack of vector bundles (on a curve) over a strictly semi-stable point of the moduli space
Consider the stack $Bun_{r,d}^{ss}$ of rank $r$ semi-stable vector bundle of degree $d$ over a fixed curve. There exists also a coarse moduli space $M$ built via GIT. Over the stable locus of $M$ it i …
- 3,779
3
votes
0
answers
130
views
state of the art for kodaira dimension of $\overline{\mathcal{M}}_{g,n}$
What is the state of the art about the kodaira dimension (and rationality, unirationality, etc.) of the moduli spaces of $n$-pointed curves of genus $g$? When it is known and when not? It would be gre …
- 3,779
3
votes
0
answers
224
views
How can one check that two line bundles on $\overline{M}_{0,n}$ coincide?
Let $X$ be the Deligne-Mumford compactification of $\mathcal{M}_{0,n}$. Suppose I have two (big) line bundles $L$ and $L'$ on $X$ and that I want to show that they are the same element of $Pic(X)$. Of …
- 3,779
3
votes
1
answer
401
views
$\psi$ class in $\overline{M}_{0,n}$
Basic question, but I found no reference.
Is the $\psi$ class the only one which is not a boundary class in the PIcard group of the Deligne-Mumford compactification of $\mathcal{M}_{0,n}$? Or can it …
- 3,779
3
votes
2
answers
331
views
blow up of segre primal and $\mathcal{M}_{0,6}$
The segre cubic primal $X\subset P^4$ is the GIT quotient of 6 points on $P^1$. Let $M_{0,6}$ the DM compactification of the moduli of 6-pointed rational curves. The Segre primal $X$ is a cubic 3-fold …
- 3,779
3
votes
1
answer
314
views
deformations of vector bundles on curves
Let $X$ be a smooth algebraic curve. Suppose I have a flat family $V_y\to X$ of vector bundles on $X$ over an affine scheme $S$. Let $p=Spec(k)$ be one geometric point of $S$. If the determinant of $V …
- 3,779
3
votes
0
answers
116
views
Families of trigonal curves with hyperelliptic limit
Suppose I have a family of trigonal curves $C\to D$ over a closed disk $D$ where the central fiber $C_0$ is hyperelliptic (this is of course possible since the hyperelliptic locus is in the closure of …
- 3,779