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12
votes
0answers
529 views

Pencils with many completely decomposable fibers

Let $F= \frac{G}{H} : \mathbb P^n \to \mathbb P^1$ be a non-constant rational function ($G$ and $H$ homogenous polynomials of the same degree in $\mathbb C^{n+1})$. The fiber over $(\lambda:\mu) \in ...
8
votes
0answers
222 views

Krull rings and determinantal invariants

During another attempt to come to grips with Hillman's excellent book Algebraic Invariants of Links, I am having difficulty figuring out why Krull rings are the setting for Chapter 3- the natural ...
7
votes
0answers
166 views

what's the role of $H^{p}(\mathbb{R}^{n})$ in modern (harmonic) analysis?

The classical theory of $H^p$,due to it's heavy dependence on the complex function theory(such as Blaschke products), seemed to have an insurmountable obstacle barrying its extension to several ...
6
votes
0answers
544 views

“a theory of generalized Donaldson-Thomas invariants” by Joyce & Song

Is anyone else working through this paper : http://arxiv.org/abs/0810.5645 ? I am trying to verifying example 6.2 (m=2 for simplicity) using only the definitions, namely: J^{2\alpha}(\tau) = -1/4 ...
5
votes
0answers
418 views

Principal $G$-bundles as fully extended TQFTs, and $n$-representations

This is a follow up to this MO question: Fully dualizable objects in classical field theories Assuming the notation there (which in turn come from Topological Quantum Field Theories from Compact Lie ...
4
votes
0answers
147 views

Interesting commensurated subgroups of countable groups

Let $G$ be a group and let $K$ be a subgroup. Say $K$ is commensurated in $G$ if $gKg^{-1} \cap K$ has finite index in $K$ for all $g \in G$. Commensurated subgroups are an inherent feature of ...
4
votes
0answers
269 views

Example of a Grothendieck pretopology satisfying a weak saturation condition

Recall that a singleton Grothendieck pretopology (henceforth 'singleton pretopology') on a category $C$ is a collection of maps $J$ containing the isomorphisms, closed under composition and stable ...
3
votes
0answers
184 views

Seek “typical examples” for the structure of spaces with two-sided Ricci bounds

By a 1990 paper of Michael Anderson, the following is true: Theorem. Let the metric space $(X,d,p)$ be a pointed Gromov-Hausdorff limit of a sequence of complete pointed Riemannian manifolds ...
2
votes
0answers
239 views

Forgetting extra structure inducing Symmetries

This is a major edit of the original post after receiving helpful comments. It is often the case when one adds additional structure to make a problem more tractable. When one attempts to forget this ...
1
vote
0answers
274 views

Homotopy theory of schemes

I have seen the notion of Homotopy come up in several contexts in schemes. For example, the book "Lectures on Motivic Cohomology" by Mazza, Weibel and Voevodsky uses this language to some extent. I.e. ...
1
vote
0answers
114 views

Algebraic properties of the semiring of open subsets.

Does anyone know of a useful general topological application of the algebraic properties of the semiring of open subsets of some topological space? Or examples of any such nontrivial properties at ...
1
vote
0answers
114 views

uniqueness of a limit of a pseudo convergent set

Is there an example of valued field in which any pseudo convergent set has a limit and such that this limit is unique?
1
vote
0answers
532 views

Example of smooth, proper but non-projective curve over an affine, connected base?

Would someone please give an example of a smooth, proper but non-projective curve $C/S$, where $S$ is affine and connected? I believe that whatever your example, $C/S$ must have genus $1$, admit no ...
0
votes
0answers
209 views

Example of function with a certain behavior.

Let $f: R \rightarrow R$. Consider the following properties: $(1)$ - There are positive constants $a$ and $r$ such that $\forall x, y$ $$|f(x)-f(y)|\leq a(1 + |x|^r+|y|^r)|x-y|.$$ $(2)$ - There is a ...