I would like to understand the topological type of a link of a singularity in a simple example. Consider for instance the cone ${xy-z^2=0}\subset\mathbb{C}^3$. If we set $x = x_1+ix_2, y = y_1+iy_2, z = z_1+iz_2$ then this corresponds to the $4$-dimensional real subvariety of $\mathbb{R}^6$ given...

The Cohen-Lenstra paper says the probability that the odd part of a class group being cyclic is close to 0.98. So I was thinking: can we find any conditions on a finite abelian group so that it cannot be a class group of any number field?

A tree $A\subseteq \omega^{<\omega}$ - possibly with dead ends - is pointed iff every path $p\in[A]$ has $p\ge_TA$. This lifts to two distinct notions of pointedness for closed sets in Baire space: A closed $S\subseteq \omega^\omega$ is pointable if there is some pointed $A$ with $S=[A]$. A cl...

Is there an easy proof of the following statement? $\forall$ $n>0 \in \mathbb N$, $ \exists$ $a\geq0 \in \mathbb N$ such that for any set of integers $(x_1,...,x_n)$ and $1\leq x_i \leq n$: $(x_1,\dotsc,x_n)$ is a permutation of $(1,\dotsc,n)$ if and only if: $(x_1+a)\dotsb(x_n+a)=(1+a)\dot...

Let $(X,d,\mu)$ be a separable metric measure space on which every ball has positive but finite measure. I've come across the definition of a homogeneous Fractional Hajlasz-Sobolev spaces which are defined as the collection of functions $f \in L^p_{loc}(X)$ for which there exists some $g \in L...

In his 1841 article De determinantibus, Jacobi remarked that the notation $\frac{\partial z}{\partial x}$ for partial derivatives is ambiguous. He observed that when $z$ is a function of $x,y$ as well of say $x,u$, then the coefficient $\frac{\partial z}{\partial x}$ appearing in the linear expan...