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

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Can the degree of an affine variety increase after intersecting with a hyperplane?

Say we have an affine variety $V \subset \mathbb{C}^n$, and suppose we intersect $V$ with a hyperplane $H$, possibly not in general position. Is it possible for the degree of $V \cap H$ to be larger t …
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