# Tagged Questions

23 views

### Show that $\dim_\Bbb C \mathcal V_p=N-\text{rank}_\Bbb C\left ( \dfrac{\partial \rho}{\partial \overline{Z_j}}(p,\overline{p}) \right )$

I'm learning about Real Submanifolds in $\Bbb C^N$ (from Baouendi's book - page 7): For $p \in \Bbb C^N$ it is customary to denote by $T_{p}^{1,0}\Bbb C^N$ the space of holomorphic tangent vectors ...
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### Intuitively what is it if making a modification of a torus?

It is well-known that if we have a equivalence relation in $\mathbb{R}^2$:$(z_1,z_2)\sim (z_1',z_2')$ iff \begin{pmatrix} z_1'\\ z_2' \\ \end{pmatrix}=\begin{pmatrix} 1&0\\ 0&1 \\ ...
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### Siegel upper-half space

In dimension 1, the Siegel upper-half space $\mathbb{H}=\{\tau\in\mathbb{C}:\Im\tau>0\}$ has the property that if $\lambda\in\mathbb{C}^\times$, then $a\lambda\in\mathbb{H}$ for some ...
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### Eigenvalue of a form

I came across the following matrix while reading an article..Can you please help me to understand the following. We are defining following form: ...
328 views

### Holomorphic function of a matrix

A statement is made below. The questions are: (a) Is the statement true? (b) If it is, does it appear in the literature? Here is the statement. For any matrix $A$ in $M_n(\mathbb C)$, write ...