Recently I learnt that $$\DeclareMathOperator{\diam}{diam}\DeclareMathOperator{\per}{per}\DeclareMathOperator{\area}{area} \inf\frac{\diam(C)(\per(C)-2\diam(C))}{\area(C)}=0$$ where the infimum is taken over all plane convex bodies $C$ (say, with non-zero area). In other words, there is no non-tr...
For the quotient space $G=G_0/G_1$, knowing the homotopy groups of $G_0$ and $G_1$, one can determine homotopy groups from the long exact sequence $$ ... \to \pi_n(G_1) \to \pi_n(G_0) \to \pi_n(G_0/G_1) \to \pi_{n-1}(G_1) \to \pi_{n-1}(G_0) \to \pi_{n-1}(G_0/G_1) \to .... $$ But in pract...
We work over an algebraically closed field of characteristic zero. Let $X$ be a Fano variety, and $T\cong \mathbb{G}_m^r$ a torus acting faithfully on $X$. I think we can canonically linearize the action of $T$ on $-K_X$. Is anything known about the GIT quotient for this action? Is the semi-sta...
I suggest to burninate discrete-series. It has 7 occurrences at the time I'm writing. 4 of them are concerned with the meaning of discrete series in the context of the classification of unitary representations of semisimple Lie groups or analogues (the "space" of irreducible unitary representa...
As the image presented below, the reddish point set is totally separated from the blueish one and the greenish one, while the blueish point set is quite mixed with the greenish one. A number of point sets on the plane. Each point set takes up a simply connected domain concave or convex. The poi...
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