All Questions

Question. Let $S$ be a non-singular complex projective surface and let $S^{[n]}$ be its Hilbert scheme of $n$ points. Is there a natural way to associate to a Kähler metric $\omega$ on $S$ a Kähler ...

Let $\{X_i\}$ be a sequence of closed irreducible $k$-dimensional subvarieties of $\mathbb{C}\mathbb{P}^n$ of degree $d$ (they may be assumed to be smooth if necessary). Assume that this sequence ...

Let $X$ be a projective variety over $\mathbb C$ and $T$ an irreducible projective $\mathbb C$-scheme. Let $a,b$ be closed points of $T$. Suppose we have a flat family $Z\to X\times T\to T$ such that ...

If S is a noetherian scheme and π : Z → X a morphism of S-schemes, where X is proper over S and Z is quasi-projective over S, then the set-valued contravariant functor $\Pi_{Z/X/S}$ on locally ...

EDIT: migrated to MSE. I am looking to get a more concrete understanding of the Hilbert scheme of projective subvarieties, specifically over $\mathbb{C}$, and to obtain good references on this subject....

Let $\{Z_i\}_{i=1}^\infty$ be a sequence of smooth irreducible $k$-dimensional submanifolds of $\mathbb{C}\mathbb{P}^n$ which converges to a closed subscheme $Z$ in the sense of the Hilbert scheme of $...