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These are "type A quiver cycles" (a name chosen so as not to collide with type A quiver varieties, which involve taking quotients; here the quotient would be a point). Your guess for the closure is co …

First, one can resolve the Schubert varieties using Bott-Samelson manifolds, and discover that any two resolutions give the same class upon pushforward. (This good situation ends with K-theory, i.e. i …

The paper by Agnihotri and Woodward, Eigenvalues of products of unitary matrices and quantum Schubert calculus, uses a Narasimhan-Seshadri correspondence between parabolic bundles and unitary connecti …

There are several rings-with-bases to get straight here. I'll explain that, then describe three serious connections (not just Ehresmann's Lesieur's proof as recounted in the OP). The wrong one is $Rep …

I'd say it's closer to an oriented manifold with corners (corners happening where the divisor is singular), or even that times a coefficient. In these papers Khesin, Rosly, and later Thomas build a ho …

What these have in common is that they are of the form $G/P$ for $P$ a maximal parabolic. As such each has a minimal projective embedding of the form $G/P \hookrightarrow \mathbb P(V_\omega)$ where $V …

There are of course two moment maps to vary - the complex one and the real one. In most treatments of quiver varieties one fixes the complex level set to be zero and the real level set to a nonzero mu …

The Schubert classes on $G/P$ are the classes of the Schubert varieties, which are the closures of the Schubert cells, each of which contains a unique $T$-fixed point. The $T$-fixed points on $G/P$ ar …

Flag manifolds $G/B$ are nice: the Kähler cone is the positive Weyl chamber, with edges coming from the Poincaré duals of the Schubert divisors.

Pull back the equation $[W] = [H]^{codim\ W} \in \mathbb P^N$. This cohomological pullback is computable set-theoretically, as $[W\cap G]$, if the intersection is transverse.

By "coadjoint orbits" I assume you mean "of a compact Lie group, but then endowed with invariant complex structures". In which case the answer is no. There is a flat family whose general fiber is $\ma …

Fix a base ring $R$, and consider pairs $(X,f)$ where $X$ is a scheme of finite type over $R$ and $f:X\to R$ is an $R$-valued algebraic (not constructible!) function on $X$. I want to consider a Grot …

This non-answer grew too long for a comment. Let's change coordinates, $B_i = \check\rho(t)A_i$, where $\check\rho(z)$ is the diagonal matrix $diag(t,t^2,t^3,\ldots,t^n)$. Then the original equations …

Yes. I assume that your $M_n$ is what is more usually denoted $\overline{M_{0,n}}$. Then the answer is yes, there is a natural map $\overline{M_{0,n}} \twoheadrightarrow M_L$, for each $L$. Specifica …

In general if $T$ acts on a projective variety $X$ with moment polytope $\Phi(X)$, then a general point $x\in X$ will have $\Phi(\overline{T\cdot x}) = \Phi(X)$ i.e. be an abnormal toric variety with …