# Tagged Questions

Complex geometry is the study of complex manifolds and complex algebraic varieties. It is a part of both differential geometry and algebraic geometry.

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### Let $f(w)=\frac{w(1-i)-(i-1)}{w-1}$, where $w$ is the left hand plane. What is the image of this map?

Let $$f(w)=\frac{w(1-i)-(i-1)}{w-1}$$, where $w$ is the left hand plane. What is the image of this map? The answer should be $|z|^2<2$ if I did everything before correctly. This is a show ...
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### Solving inequality in complex plane

I have to graphically represent the following subset in the complex plane being z a complex number: $A={1<|z|<2}$ However after trying to do it on WolframAlpha it says that "inequalities are ...
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### How to interpret the cotangent bundle of a complex manifold?

Let $X$ be a complex manifold. I am not sure what people mean when they talk about the cotangent bundle $T^*X$ of $X$. I have two interpretations: At each point $x\in X$, $T_x^*X$ is the complex ...
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### Is the complementary of a 2 codimensional set in a complex space simply connected?

It is well-known that if X is a complex manifold and $A \subset X$ an analytic set of codimension at least $2$ then $\pi_1(X)=\pi_1(X\setminus A)$. Can we generalize this equality when $X$ is a ...
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### Verlinde Formula in geometric quantization?

I think I have a fair grasp on the $\rm{SU}(2)$ Verlinde Formula from the algebraic geometry perspective. I'm hoping to understand better how exactly this relates to the geometric quantization of a ...
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### Equation of the form $\overline{\partial}_{J}f=g$ made holomorphic

In section 2.6 of the book "Holomorphic curves in symplectic geometry" by Audin and Lafontaine there is explained when one can transform a perturbed holomorphic curve in a holomorphic curve. I tried ...