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Results tagged with complex-geometry
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user 134494
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
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Rank of a tangent map related to holomorphic line bundles
Let $L,\,\,J$ be two holomorphic line bundles over a compact Riemann surface $X$ of genus $g_X>0$ such that
(1) $d_1:=\dim H^0\big(\operatorname{Hom}(L,J)\big)>0$ and $d_2:=\dim H^0\big(\operatorname{ …
- 391
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Extension of holomorphic line bundles
Let $E$ be a rank two holomorphic vector bundle, consider the following extension of two holomorphic line bundles
$$
\mathbb{E}:\ 0\rightarrow S\stackrel{j}{\rightarrow}E\stackrel{g}{\rightarrow} Q\ri …
- 391
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Concise expression for a specific holomorphic map $f:D\times D\longrightarrow \mathbb{B}^{2}$
Let $\mathbb{B}^{2}\subset \mathbb{C}^{2}$ be the unit ball and $D=\{z\in\mathbb{C}:|z|<1\}$. $f=(f_{1},f_{2}):D\times D\longrightarrow \mathbb{B}^{2}$ is a holomorphic map satisfying $\{det df=0\}\su …
- 391