# Tagged Questions

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### a corollary of Cauchy's integral formula in several complex variables

I'm learning several complex variables. There is a corollary of Cauchy's integral formula that I don't know how to prove. Let $X\subset\mathbb{C}^n$ be a domain. For each multi-index $\nu$, for each ...
Suppose $D=\Delta^n(a,r)=\Delta(a_1,r_1)\times \ldots \times \Delta(a_n,r_n) \subset \mathbb{C}^n$ and $\Gamma =\partial \circ \Delta^n(a,r)=\left \{ z=(z_1, \ldots , z_n)\in ... 1answer 48 views ### Sheaf on a Stein variety such that$H^{1}(X, \mathcal{F}) \neq 0$I would like to find a non-coherent sheaf on a Stein variety$X$such that$H^{1}(X, \mathcal{F}) \neq 0$. Does anyone know any example? Thank you! 0answers 69 views ### Holomorphic function vanishing in a real hyperplane A real hyperplane of$\mathbb{C}^{n}$is given by a equation$\textrm{Re}( \ell(Z)) = c$, where$c \in \mathbb{R}$and$\ell(Z) = \sum_{j=1}^{n} a_{j}z_{j}, a_{j} \in \mathbb{C}$. How to prove that if ... 1answer 125 views ### A sequence that tell us if a holomorphic function of several variables is identically zero Is there any sequence$\{ Z_{\nu} \}_{\nu \in \mathbb{N}}$in$\mathbb{C}^{n}$,$Z_{\nu} \rightarrow 0$, such that any holomorphic function in$\mathbb{C}^{n}$which vanishes in$Z_{\nu}$for all$\nu ...
I am reading Gunning's book Introduction to Holomorphic Functions of Several Variables, Vol. I, and I am stuck in the proof of Maximum modulus theorem: if $f$ is holomorphic in a connected open subset ...