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3 votes

Can Schubert cells be defined, set theoretically, by less equations then the standard ones?

The dimension of $Gr(V,2)$ is $2 (n-2)$. For each point $x$ of $Gr(V,2)$ not in $\Sigma(U)$, the codimension of the space of subspaces $L$ that vanish on $x$ in the space of $m$-dimensional subspaces …
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2 votes
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"Degree" of a Fano Scheme of a projective variety

There is a natural $\mathbb P^k$-bundle on the Grassmanian, with a natural map to $\mathbb P^n$. Pull back your cycle to the bundle, then push forward to $\mathbb P^n$.
Will Sawin's user avatar
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