MathOverflow

Let $X$ be an affine algebraic surface. If $X$ has embedding dimension (i.e. the number of elements of a minimal generating set) $n$ then the ideal of relations has at least $n-2$ generators, with equality precisely when $X$ is a complete intersection...

Let $G$ be a finite group, and let $T_1,T_2 \le G$ be conjugate subgroups. Set$$A := T_1T_2 \cap T_2T_1.$$
For a subset $S \subseteq G$, let $M_S$ denote the operator on $\mathbb{C}[G]$ defined by$$(M_S f)(x) := \sum_{s\in S} f(xs).$$I will refer to the multiset of eigenvalues of $M_S$ (counted with multiplicity) as the spectrum of $S$....

Brouwer's fan theorem is the standard result that the Cantor space is compact, or equivalently that the Cantor space viewed as a locale is spatial. Since it is a compactness result for a countable product of spaces, it can be viewed as a countable choice...

The celebrated Chevalley–Shephard–Todd theorem says that $\mathbb C[V]^{S_n}$ is a polynomial algebra and gives the generators of this algebra, where $V$ is the standard (or natural) representation of the symmetric group $S_n$. I am just curious to know...