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Results tagged with moduli-spaces
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user 43639
Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.
3
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Resolving structure sheaf of diagonal via universal bundle on moduli space
To study the geometry of the moduli space $\mathcal M$ of semi-stable sheaves on a variety $X$ with fixed Hilbert polynomial, it is useful to have a locally free resolution of the structure sheaf $\ma …
- 1,980
9
votes
1
answer
1k
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Reference request: tangent space to moduli space of coherent sheaves is $\operatorname{Ext}^...
Is there a standard reference for the fact that, in an appropriate algebraic-geometrical context, the tangent space at the point $[E]$ to the moduli space $\mathcal M$ is something like $\operatorname …
- 1,980
6
votes
Accepted
Reference request: tangent space to moduli space of coherent sheaves is $\operatorname{Ext}^...
Theorem 2.6 (page 9) from Hartshorne Lectures on Deformation Theory (it seems that Hartshorne uses the same notation both for an affine scheme $D$ and its function algebra):
Let $X$ be a scheme over …
- 1,980
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answers
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How to calculate the top Chern class of a "functorial" vector bundle on a moduli space of sh...
Let $\mathcal M$ be a moduli space of sheaves on a nice variety $X$, with fixed rank $r$ and Chern classes $c_i$, semi-stable with respect to an ample bundle $H$. Let $E$ be a "functorial" vector bund …
- 1,980
26
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Why there is a Quot-scheme, not a Sub-scheme?
Let $X$ be a projective variety, and $E$ be a coherent sheaf on $X$. Grothendieck has proven that there is a scheme $\mathrm{Quot}_X(E)$ parametrizing arbitrary quotient sheaves of $E$. It is probably …
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