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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.

9 votes
2 answers
598 views

When is a formal deformation convergent?

Let $X$ be a finite type scheme over $\mathbb{C}$ and let $ \mathcal{X} \to Spf(\mathbb{C}[[x]])$ be a formal deformation of $X$. Which of the following assumptions (or combinations thereof) are suffi …
Saal Hardali's user avatar
  • 7,799
9 votes
1 answer
835 views

Algebro-geometric version of {vector fields} $\longleftrightarrow$ {flows} correspondence?

Main Question: What Is the correpondence between flows and vector fields in algebraic geometry? Here is a more precise statement could be an answer If it was true (I have no idea it is): "P …
Saal Hardali's user avatar
  • 7,799
7 votes
0 answers
483 views

A general definition of an equisingular family of singular varieties?

This question is about the existence of a definition. I'm far from being an expert in the field in question I apologize in advance for any inaccuracies or stupid and wrong assumptions. Let $X$ be a s …
Saal Hardali's user avatar
  • 7,799
7 votes
1 answer
1k views

Can the homological dimension of a coherent sheaf explode along a formal deformation? (is th...

Let $X_0$ be a locally noetherian scheme and $\mathcal{F}_0$ a coherent $\mathcal{O}_{X_0}$-module. Let $C$ be an artin ring with residue field $k$ and let $X \to Spec C$ be a (flat) deformation of $X …
Saal Hardali's user avatar
  • 7,799