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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.
2
votes
Moduli spaces and conic bundles
here
https://arxiv.org/pdf/1409.5033.pdf
in section 5 there's an example of unirational, non-rational, 3fold moduli space. I am not sure whether it is a conic bundle, though. Probably not.
- 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?
- 66.3k
2
votes
1
answer
142
views
Fiber of the Prym map in dim 2
This must be very classical, but I can't find a reference.
Is there an explicit description of the (generic?) fibers of the Prym map $\mathcal{R}_3 \to \mathcal{A}_2$?
By this I mean the map t …
- 66.3k
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
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
1
vote
Trigonal loci in Teichmueller spaces
The trigonal locus in the Teichmuller space - under mild hypotesis - is connected. The answer follows from one of the main results of
http://arxiv.org/abs/1403.7399
- 3,779
0
votes
0
answers
186
views
projective map from $\overline{\mathcal{M}}_{0,n}$
Suppose I have a morphism $f:\overline{\mathcal{M}}_{0,n} \to \mathbb{P}^N$ birational onto its image, and I know exactly what $F$-curves are contracted (or "dually", what divisors are contracted). Su …
- 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 …
- 16.2k
1
vote
0
answers
139
views
symmetric theta structures and arithmetic subgroups
A symmetric theta structure is a theta structure that commutes with (a lift of) the natural involution $\imath: A \to A$ an an abelian variety. For simplicity I will assume that $A$ is a surface.
Now …
- 3,779
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
1
vote
1
answer
145
views
divisors on $\overline{\mathcal{M}}_{g,n}$ that are trivial on certain $F$-curves
Inside the moduli space of curves $\overline{\mathcal{M}}_{g,n}$ one can distinguish two classes of $F$-curves isomorphic to $\mathbb{P}^1$: those of type $\overline{\mathcal{M}}_{0,4}$, and those of …
- 4,111
2
votes
2
answers
516
views
spin bundle vs. hodge bundle
Let $\overline{\mathcal{M}}^r_{g,n}$ the space of $n$ pointed $r$-stable curves of genus $g$, endowed with a root of the canonical sheaf, and let $\mathcal{C} \to \overline{\mathcal{M}}^r_{g,n}$ be th …
- 40.2k
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 …
- 8,004
2
votes
1
answer
256
views
picard group of moduli of elliptic r-prym curves
Let $\overline{\mathcal{M}}_{1,1}$ be the DM compactification of the moduli stack of elliptic curves. Its Picard group is $\mathbb{Z}$. Let us now consider stack of $r$-prym curves $\overline{\mathcal …
- 40.2k
2
votes
0
answers
385
views
branch locus of the discriminant map $\overline{\mathcal{H}}_{g',r} \to \overline{\mathcal{M...
Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of pointed, stable, genus $g$ curves. Let $\overline{\mathcal{H}}_{g',r}$ be the hurwitz space of cyclic covers of degree $r$ of genus $g$ curves …
- 3,779