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Results tagged with ag.algebraic-geometry
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user 37
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
0
votes
are deformations of torsion modules always torsion?
[I'm going to work over k[h] as the base instead; I don't think anything changes, but if I'm wrong you should let me know.]
Consider the case M = k[s,t,h]/(st-h^2). Setting h=0 yields M_0 = k[s,t]/( …
- 916
5
votes
Accepted
If $\Omega_{X/Y}$ is locally free of rank $\mathrm{dim}\left(X\right)-\mathrm{dim}\left(Y\ri...
I think Ishai's example is close, but one must be a little careful; the normalization of the node is a good example, but the normalization of the cusp is ramified, and the sheaf of relative differenti …
- 916
11
votes
What is the universal property of normalization?
Normalization is right adjoint to the inclusion functor from the category of normal schemes into the category of reduced schemes. In other words, if $n:Y\rightarrow X$ is the normalization of $X$ and …
- 916
20
votes
Accepted
What is the universal property of normalization?
I've realized that my answer is wrong. Here's the right answer: if $Z$ is a normal scheme and $f: Z \to X$ is a morphism such that each associated point of $Z$ maps to an associated point of $X$, the …
- 916