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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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How to define the intersection multiplicity of a projective variety and a complete intersect...

In the appendix of Algebaric Geometry by Hartshorne, he shows us that how Serre defines the intersection number in a more general case:$$i(X,Y;Z)=\sum(-1)^i\cdot\bigl(\operatorname{length} \operatorna …
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