Questions tagged [moduli-spaces]
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.
964 questions
0
votes
0
answers
111
views
Fine moduli space of elliptic curves(level 3). Applications?
Recently I have learned that there is a fine moduli space for elliptic curves $X$ with fixed morphism $\phi: (\mathbb{Z}/3\mathbb{Z})^2 \rightarrow X[3]$. In Dolgachev's "Classical Algebraic ...
1
vote
0
answers
95
views
Isomorphism types of curves in the second Hirzebruch surface
I am not well versed in algebraic geometry but am trying to learn about certain linear systems over the 2nd Hirzebruch surface. I would appreciate any references to where I can learn about this kind ...
- 29
1
vote
0
answers
126
views
Do set-theoretical freeness of an additive $\mathbb C^+$ group action + geometric quotient imply properness?
Let $\mathbb G_a=\mathbb C^+$ denote the additive group scheme over $\mathbb C$. Suppose we have an affine complex variety $X$ and a set-theoretically free $\mathbb G_a$ action on $X$ that admits a ...
- 643
9
votes
0
answers
382
views
Yang-Mills theory and... reciprocity laws!
This question is about two papers which I do not understand. Ergo, most probably it does not make any sense.
I am, moreover, no number theorist; -- and, hence, would be very glad if someone more ...
- 487
4
votes
0
answers
55
views
Computing the universal family for a moduli problem
Fix $n\ge 0$. I'm interested in understanding a compactification of the moduli of ordered $n$-tuples
$$(a_1,\dots,a_n)\in\mathbb R^n,\qquad a_1\ge \cdots \ge a_n,$$
taken modulo the diagonal ...
- 91
2
votes
0
answers
100
views
Limit of Higgs bundles
Let $X$ be a smooth complex projective surface, let $\mathcal{M}$ be the moduli space of semistable Higgs sheaves with fixed Hilbert polinomial with respect to a polarization of $X$.
There exists a ...
- 990
1
vote
1
answer
232
views
Family of vector bundles over a relative A^1
Let $A=\mathbb{C}[[s]]$, I am looking for an example of a non-trivial vector bundle (or $\operatorname{SL}_n$-torsor) on $\mathbb{P}^{1}_{A[t,t^{-1}]}$ that is trivial over $\mathbb{P}^{1}_{\mathbb{C}...
- 3,622
3
votes
1
answer
397
views
Is it true that $\operatorname{Alb}(X \times Y ) \cong \operatorname{Alb}(X) \times \operatorname{Alb}(Y) $?
$\DeclareMathOperator\Alb{Alb}\DeclareMathOperator\Pic{Pic}$Let $X$ and $Y$ be two smooth projective varieties over $\mathbb{C}$. My question is, is it true that,
$$\Alb(X \times Y ) \cong \Alb(X) \...
- 317
3
votes
1
answer
333
views
For a smooth projective curve $X$, is the map, $M(r,d)\rightarrow \mathrm{Pic}^d(X)\cong \mathrm{Pic}^0(X)$ an albanese morphism?
$\DeclareMathOperator\Pic{Pic}$Let $X$ be a smooth projective curve and $M(r,d)$ be the moduli space of semistable vector bundles of rank $r$ and degree $d$ over $X$. My aim is to show that, when we ...
- 317
2
votes
1
answer
245
views
Variants of moduli spaces of Riemann surfaces
The moduli space $M_{g,n}$ of genus $g$ Riemann surfaces with $n$ marked points is well-studied and is finite-dimensional. I'm curious about the moduli space $M_{g,\vec{n}}$ of genus $g$ Riemann ...
- 967
1
vote
0
answers
146
views
What is Baer's theorem?
I've been reading the paper "The global nilpotent variety is Lagrangian" by Ginzburg, which aims to show that for the stack of Higgs $G$-bundles over a curve $X$, which is isomorphic to the ...
- 83
4
votes
1
answer
222
views
Stack quotient of a point vs. classifying spaces
I want to work over the site of smooth manifolds with Grothendieck topology induced by open immersion. I am primarily concerned with the the following question: in what ways can we classify vector ...
- 705
4
votes
1
answer
280
views
Isomorphism between Moduli spaces of vector bundles with fixed determinants, over a curve
Let C be a smooth projective curve, and let $L_1$ and $L_2$ be two line bundles with degree $d_1$ and $d_2$ respectively, where $gcd(r,d_i)=1$ for $i=1,2$. Suppose $M(r, L_1)$ and $M(r, L_2)$ are two ...
- 317
1
vote
2
answers
446
views
On properties of quotients on the form $G \rightarrow G/H$ for $H \subseteq G$ a closed subgroup scheme
Let $A$ be any commutative unital ring and let $V:=A\{e_1,..,e_n\}$ be the free rank $n$ $A$-module on the basis $B:=\{e_i\}$. Let $1 \leq d_1 < \cdots < d_k < n$ be integers and let $V_i:=A\{...
- 463
8
votes
0
answers
273
views
Dévissage in o-minimal structures
In his Esquisse d’un programme Grothendieck advocated a new foundations for topology making it more apt for geometry (…I'm far away from seeing completely through what Grothendieck meant exactly by &...
- 4,142