# Tagged Questions

204 views

### Does the following object has a name in algebraic geometry?

Suppose $X$ is a projective variety and $D$ is a smooth divisor and let $L = \mathcal{O}(D)$ be the line bundle corresponding to $D$. Consider $X \times \mathbb{P}^1$ with the line bundle ...
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### Geometric interpretation for fourth coeficient of the polynomial for Hirzebruch–Riemann–Roch theorem

Hey guys :) I have a question on a theorem which is known as Tian-Yau-Zelditch theorem now. If there is some reference for following question, please let me know Let $(M,\omega)$ be a compact ...
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### When $\frac{\text{Aut}(G/P,L)}{S^1}$ is discrete?

Let $(M,\omega)$ be a Kähler manifold with a pre-quantum Line bundle $L$ and $\text {Aut}(M,L)$ means the group biholomorphisms of $M$ which lift to holomorphic bundles maps $L\to L$. My question is ...
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### Distribution of random Projections on the Stiefel Manifold

Imagine we have an $m$-Frame in $\mathbb{C}^n$ uniformly distributed on the stiefel manifold. That is: $\mathbf{U}\in\mathbb{C}^{n\times m}$, $m<n$ and $\mathbf{U}^H\mathbf{U}=I$ and $U$ has a Haar ...
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### when is an irreducible SL_2(C) representation of a cusped hyperbolic 3-manifold scheme reduced or smooth

Let $M$ be an orientable cusped hyperbolic 3-manifold. Let $\rho \in hom(\pi_1(M),SL_2(\mathbb{C}))$ be an irreducible representation. Is $\rho$ scheme reduced ? What can prevent $\rho$ from being ...
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### moduli space of equivariant holomorphic embeddings into the quintic

I'd like to understand better the following problem, whether it is mathematically well-posed, trivial, etc. Fix a non-negative integer $g$ and consider the space ...
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### Relation between Milnor ring and middle dimensional homology of hypersurface

I have suspected that the following is well-known: If $P$ is a homogeneous polynomial of degree $d$ in $n$ variables (for example, Fermat quintic $x_1^5 + \cdots + x_5^5$). The Milnor ring is ...
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### Origin of the name “Torelli group”

The genus $g$ Torelli group $I_g$ is the kernel of the action of the mapping class group of a genus $g$ surface on the first homology group of the surface. The first paper I am aware of that uses the ...
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### Is there a good notion of morphism between orbifolds?

Following Thurston, an orbifold is a topological space which looks locally like a finite quotient of $\mathbb R^n$ by a finite group of $O(n)$: this is expressed using charts as for differentiable ...
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### topology on varieties

Let $X, Y$ be varieties over $\mathbb{C}$, and the topology I am talking about is the Eucliden topology. I am not sure if the following two results are true, and where can I find the references: (1) ...
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### looking for an identity for higher jet bundle $J^kM$?

We know this fact that the first jet Bundle $J^1M$ is diffeomorphic with $T^*M×\mathbb{R}$.i.e, ($J^1M=T^*M×\mathbb{R}$) Is there something like this identity for higher jet bundle $J^kM$? I editted ...
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### moduli spaces are kahler?

I often heard from experts that "moduli spaces are Kahler". This sounds as a meta-theorem asserting that every time one defines reasonable moduli spaces, then there is a standard strategy to see ...
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### Fractional degree of a map?

Is there some natural notion of a fractional degree of a map? The degree of a map is a generalization of the winding number, and fractional winding numbers appear in the (mathematical physics) ...
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### On complex surfaces with Kodaira dimension 1

Let $S$ be a complex surface of Kodaira dimension $1$ and $\pi_{1}(S) \neq 1$. What is known on possible diffeomorphism types of such $complex$ surfaces with a given fundamental group? Is it true ...
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### Covering seifert manifolds

Let $M$ be a 3-manifold with boundary. If $M$ has an orientable finite cover that is a Seifert fiber space, then is $M$ also a Seifert fiber space?
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### Complex structure of the Teichmüller space in terms of Fenchel-Nielsen coordinates

The Teichmüller space $T_g$ of genus $g$ Riemann surfaces can be parameterized in terms of Fenchel-Nielsen coordinates, taking values in $\mathbb{R}^{3g-3}\times \mathbb{R}_+^{3g-3}$. The ...
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### Generators for exact representations of 3-manifold groups

Does anyone have a list of matrix generators for a bunch of hyperbolic 3-manifold groups? I am testing an algorithm and am looking for a collection of test cases. I am looking for exact values of ...
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### Relationship between virtual cohomological dimension and tautological rings for moduli spaces of curves

Here's the short version of the question. For $M_{g,n}$, $M_{g,n}^{rt}$, $M_{g,n}^{ct}$ and $\overline M_{g,n}$ it seems that the virtual cohomological dimension is given by the complex dimension plus ...
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### Is surface $x^2+z^2=2\cdot y^2$ something of a Möbius strip?

This question is naive. My association with Möbius strip comes from not being able to smoothly extract positive solutions of the diophantine equation $$x^2+z^2=2\cdot y^2$$ I got a parametrization ...
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### On the simply connectedness of Symmetric products and Hilbert schemes of points

My first question is whether $m$-th symmetric product of $\mathbb{C}^{n}$ is simply connected, where $n\geq 3$. The second question is whether $Hilb^{m}(\mathbb{C}^{n})$ is simply connected, where ...
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### What is Kirillov's method good for?

I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory important for ...
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### Algebraic Stratifications of $G$-varieties

My question is simple: Given an algebraic group $G$ acting on a variety $X$ algebraically. If the orbits are of finite number then they form what is called an algebraic stratification of $X$. Now my ...
Hello, Suppose that $C_1,C_2\subset\mathbb P^2$ are projective curves (over $\mathbb C$); $C_1$ and $C_2$ may be reducible but they must not have a common component. Let $L\subset \mathbb P^2$ be a ...