# Tagged Questions

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### Some examples of $\mathbb Q$-Gorenstein smoothing

I am trying to understand $\mathbb Q$-Gorenstein smoothings, and especially the third condition in the following definition. Definition. For a normal projective surface $X$ with quotient ...
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### Surjectivity of the Kodaira-Spencer map

Let $X$ be a complex projective manifold. Let $B$ be the closed subscheme of $H^1(X,T_X)$ defined by $\mathfrak{m}^2$, where $\mathfrak{m}$ is the ideal defining the origin. In other words, $B$ is a ...
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### 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): "...
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### Cohomology of tangent sheaf of a singular hypersurface

Let $X\subset\mathbb{P}^n$ be a hypersurface singular at finitely many points $p_i\in X$. We may assume that $X$ has ordinary singularities at the $p_i$'s. Does there exists a formula, perhaps in ...
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### Deformation Quantization

I am a beginner and I want to learn about deformation quantization. Please suggest me with which book or notes, I should start?
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### Questions (related to deformation theory?) about modular ideals in mod ell Hecke algebras

I suspect that I'm asking (familiar?) questions from deformation theory in a different language. But I'm an illiterate in deformation theory language; if my suspicion is correct I'd be grateful for an ...
Let $S$ be a smooth quasi-projective curve over the complex numbers. Let $P$ be a closed point in $S$. Let $f:\mathcal X \to S$ be a polarized family of smooth projective connected varieties. To this ...
### Inverse Galois problem for $GL_2$ of a compact local ring
Let $A$ be complete noetherian local ring with maximal ideal $m$ and residue field $A/m$ a finite field (in other words, $A$ is a noetherian compact local ring) For which $A$ as above is there a ...