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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 ...
1 vote

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 ...
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 $h$" ...
4 votes

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

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 ...
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