All Questions
7 questions
29
votes
1
answer
4k
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Almost Complex Structure approach to Deformation of Compact Complex Manifolds
I don't know much about the deformation of compact complex manifolds, I've only read chapter 6 of Huybrechts' book Complex Geometry: An Introduction. There are two parts to this chapter. The second ...
- 19.3k
15
votes
1
answer
3k
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Kodaira-Spencer theory of deformation done right
I thought in asking this question on Math StackExchange, but by my experience I don' t think anyone will notice me. Recently, I started studying deformation of complex manifolds in the sense of ...
- 2,227
8
votes
1
answer
431
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Holomorphic deformation of complex structure on the real plane
It is known that each complex structures on $\mathbb{R}^2$ is biholomorphic to either $\mathbb{C}$ or the open unit disk $\Delta$.
One can continuously deform one complex structure to the other as is ...
- 1,409
6
votes
1
answer
2k
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Kodaira Spencer map and versal deformation
First I want to clarify what I mean by the Kodaira-Spencer map.
Let's have a family of deformations $\pi:\mathcal{X}\rightarrow B$ of a complex manifold $X=\mathcal{X}_0:=f^{-1}(0)$ (by that I mean ...
- 175
5
votes
0
answers
189
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Extension of holomorphic maps to smooth family of holomorphic maps
Let $\pi:X \to D^2$ be a family of diffeomorphic (but not isomorphic) complex manifolds. Each fiber is allowed to have boundary but is compact (maybe not Stein) and $D^2 \subset \mathbb{C}$ is a ...
- 1,409
3
votes
0
answers
176
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Some general questions about deformations
$\newcommand{\spec}[1]{\mathrm{spec}(#1)}$
$\newcommand{\ZZ}{\mathbb{Z}}$
$\newcommand{\QQ}{\mathbb{Q}}$
$\newcommand{\CC}{\mathbb{C}}$
These days I am reading in Kurke, Pfister, Roczen "...
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2
votes
2
answers
1k
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On the algberaicity of the universal elliptic curve associated to a torsion free subgroup
So let $\Gamma\subseteq SL_2(\mathbf{Z})$ be a finite index subgroup (not necessarily a congruence subgroup). Recall that we have an action of $SL_2(\mathbf{R})$ on
$\mathbb{H}=\{z\in\mathbf{C}:\Im(z)...
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