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# Questions tagged [deformation-theory]

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

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### Theorem from Deformation Theory

My question refers to some steps it the proof of Theorem 3.3 part (b) in Christensen's paper treating Deformation theory (see pages 9-11): https://mathematics.stanford.edu/wp.../A.-Christensen-Draft....
235 views

### Obstructions to locally trivial deformations

Let $X$ be a complex projective variety. If $X$ is smooth, then the first-order infinitesimal deformations are given by $H^1(X, T_X)$ and the obstructions are in $H^2(X, T_X)$. Now assume that $X$ is ...
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### non-associative deformation quantization [closed]

Several physicists now consider non-Poisson bivectors but still apply Maxim’s morphism for deformation quantization. The result is a `non-associative star product’, So a deformation as a ________? ...
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### The underlying curve of a family of genus zero $n$ punctured curves

Let $X$ be a curve of genus zero over an algebraically closed field $k$ so that $X \cong \mathbb{P}_k^1$. Let $(C, s_1, \cdots, s_n)$ a $n$ punctured genus zero curve over $k$ where $s_i: k \to C$ are ...
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### Coarse moduli space versus Kuranishi family

We will work over complex number field $\mathbb{C}$. Let $\mathscr{M}_h$ be the moduli functor for canonically polarized manifolds with $h$ the Hilbert polynomial. Let us denote by $M_h$ the coarse ...
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### Log deformations in obstructed case

I'm going to assume reader is aware of semi-stable log structures either in Kawamata-Namikawa version or later approaches. Anyway, let $X$ be a d-semistable variety. I want to know whether I can ...
170 views

### Example of a nonsmoothable scheme

I try to understand Iarrobinos example of a nonsmoothable 0-dimensional scheme with the help of Artins notes on it: http://www.math.tifr.res.in/~publ/ln/tifr54.pdf (pages 4-6) But I have some ...

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