## New answers tagged deformation-theory

2
votes

### Is the algebra of sections of a bundle of complex Clifford algebra over an oriented Riemannian manifold rigid?

Let's try this: assume that the complex vector bundle you start with has even fiber dimension such that the corresponding Clifford algebra bundle is a bundle of complex matrix algebras. Suppose ...

- 7,529

1
vote

Accepted

### Can deformation equivalent Kähler manifolds always be obtained by a deformation where all the fibers are Kähler?

I don't think this is known. For hyperkahler manifolds, conjecturally,
all smooth complex deformations are class C and birational to hyperkahler.
If this is true, your conjecture would follow ...

- 8,323

6
votes

### Understanding definition of quantization of a Poisson-Hopf algebra

You didn't give the definition of $A_h$ but if you look there, you should see that elements of it are formal power series in the parameter $h$ with coefficients from $A$. Then "mod $h$" ...

- 1,963

4
votes

Accepted

### Deformation theoretic argument on dimension counting of naive Hurwitz scheme

You can get a lower bound on the dimension of $V_{d,g}$ using deformation theory as follows. The deformation obstruction theory of a map $f : X \to Y$ between smooth varieties (where $f$ and $X$ are ...

- 2,578

4
votes

Accepted

### Extension of first order deformations of a line bundle

Under some conditions on $X,V$, your line bundle can be extended to $X_{\varepsilon}$. Indeed, let $\imath_X:X\hookrightarrow X_{\varepsilon}$ and $\imath_V:V\hookrightarrow V_{\varepsilon}$ be two ...

- 66

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