All Questions
Tagged with complex-geometry hilbert-schemes
6 questions with no upvoted or accepted answers
9
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0
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387
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Kähler metric on the Hilbert scheme of points on a surface
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 ...
6
votes
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170
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A relation of convergence in Hilbert scheme to convergence in sense of currents
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 ...
1
vote
0
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185
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Cycle class/cohomology class of subvarieties in flat families
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 ...
1
vote
0
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205
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Space of sections
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 ...
0
votes
0
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158
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Understanding the Hilbert scheme of subvarieties of $\mathbb{CP}^n$
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....
0
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146
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Limit of a sequence of smooth varieties in Hilbert scheme
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 $...