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Results tagged with deformation-theory
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user 2757
for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
10
votes
Example of a smooth morphism where you can't lift a map from a nilpotent thickening?
Let $Y=\operatorname{Spec} k$ and let $X=\mathbb{P}^1_k$, viewed as $\operatorname{Spec} k[t]$ glued to $\operatorname{Spec} k[t^{-1}]$.
Let $T = \operatorname{\bf Spec}(\mathcal{O}_X + \mathcal{O}_X( …
- 23.8k
24
votes
Accepted
Example of a smooth morphism where you can't lift a map from a nilpotent thickening?
Using some of BCnrd's ideas together with a different construction, I'll give a positive answer to Kevin Buzzard's stronger question; i.e., there is a counterexample for any non-etale smooth morphism. …
- 23.8k
25
votes
Is a 'generic' variety nonsingular? Or singular?
Executive summary: If you look at the whole Hilbert scheme associated to a given polynomial, the locus of points corresponding to nonsingular (which I take to mean smooth) subschemes can sometimes be …
- 23.8k