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Results tagged with complex-geometry
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user 133871
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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A contradiction caused by the Kähler identity and the formal adjoint relation
I found a contradiction in the Principle of Algebraic Geometry by G&H, section 1.2. I have post this on MSE but it didn't get enough attention. I couldn't sleep or eat or do anything else due to this …
CommunityBot
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Understanding sheaves on normalisation of a curve: $v_* \mathcal{O}_{\tilde{C}} / \mathcal{O...
Let $(C, \mathcal{O}_C)$ be a reduced irreducible curve and $(\tilde{C},\mathcal{O}_{\tilde{C}})$ its normalisation with $v : \tilde{C} \rightarrow C$. Then we have an imoprtant skyscraper sheaf $v_* …
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A contradiction caused by the Kähler identity and the formal adjoint relation
I can give a explanation. Noting that in this question $\eta$ is a harmonic form in $\Omega^{p,q}(L)$ where $L$ is a positive line bundle. And harmony means $\Delta_{\bar{\partial}} \eta =0$.
First of …
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Analytic and algebraic definitions of intersection multiplicity of two complex algebraic cur...
There are two definitions of intersection multiplicity of two complex algebraic plane curves. One of them is given in An introduction to algebraic curves by Griffiths. Let $t \mapsto (t^k, y(t) )$ be …
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