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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.
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smooth modular compactification of moduli of curves
$\mathbb{P}^3$ compactifies the moduli space of genus 2 curves with level 3 structure and the choice of an odd theta characteristic.
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1
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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
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2
votes
Accepted
Dimension of the linear system of $\psi$-class on $\bar M_{0;n}$
I think that this is done by Kapranov in "Veronese curves and Grothendiexk-Knudsen moduli space $M_{0,n}$".
The projective dimension of this linear system should always be $n-3$ (so the linear dim is …
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1
vote
Classification of first order deformations of n-pointed non-singular variety
Here's a "quick and dirty" answer, far from being precise. Take the case of curves that you mention: the idea is that , the more points that you add to your moduli problem, the more parameters you nee …
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1
vote
2
answers
362
views
one "big" Hilbert scheme?
I was recently reading one of the papers of Kapranov on $\mathcal{M}_{0,n}$ and he says that one can see it as a subvariety of the Hilbert scheme parametrizing all subschemes of a certain projective s …
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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 …
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1
vote
1
answer
267
views
glueing flat families of objects over a blow-up
Hi Everybody,
I stumbled upon the following question for families of vector bundles (over a curve) but I guess it could be interesting to answer in general.
Suppose I have $B$ the blow-up of a smoo …
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2
votes
1
answer
179
views
does there exist a family of objects over the tangent space to the base space of a family of...
Suppose we have a family of objects $\Xi \to S$ over a base smooth projective scheme $S$. Take a closed point $p\in S$ and consider the tangent space to $S$ at $p$. Can one construct an "induced famil …
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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 …
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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?
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0
votes
1
answer
616
views
universal families and maps to quotient stacks
Suppose I have a certain (contravariant) moduli functor $M:Schemes \to Groupoids$ that is represented by a quotient stack $[X//G]$ where $X$ is a scheme and $G$ a linearly reductive group. Roughly spe …
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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?
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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 …
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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 …
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2
votes
1
answer
760
views
fano moduli varieties of vector bundles
Let $M$ be a fine moduli space of vector bundles on curve which is an algebraic variety as well. The first example of such an object that I have in mind is rank 2, deg 1 VB on a genus 2 curve. This is …
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