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Let $\mathcal O$ be the structure sheaf of $\mathbb P^1$. Then $\mathcal O \oplus \mathcal O(1)$ is rigid and generates the derived category of coherent sheaves on $\mathbb P^1$. Thus, it is a tilti …

One simple answer is to talk about the totally positive part of $(G_{k,n})_{> 0}$, the part of the Grassmannian where all the maximal minors (=Plücker coordinates) are real and positive. Naively, if …

Yes. Let $\Sigma$ be the fan corresponding to $P$. Section 2.6 of Fulton's "Introduction to Toric Varieties" explains how to perform toric resolution of singularities on $\Sigma$ so as to produce a fa …

Given a manifold $M$, we consider its cotangent bundle $T^*M$, and its cocircle bundle $T^\infty M$, quotienting out by the scaling action of the positive reals. Given a Legendrian submanifold $\Lambd …

I'm going to say some things which might be either (a) obvious, (b) wrong, or (c) useless. (Or some combination!) You could rephrase the question by asking that the map from SL_k x SL_k to SL_k x SL …

A fan is a collection of strongly convex rational polyhedral cones in $\mathbb Z^n$, which we often think of as contained in $\mathbb Q^n$ or $\mathbb R^n$ for purposes of visualizing it. The defining …

I realized, after asking the question, that if the original question was known to have an affirmative answer, then that would imply the strong Oda conjecture. Since the strong Oda conjecture isn't kno …

I had a problem which may be similar when I encountered root systems for the first time. In retrospect, I think that the problem was that I was reading about specific realizations of root systems (eg …