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Degeneration of Dual Varieties of Hypersurfaces

Consider a one-parameter family of smooth projective varieties X_t which degenerate into a simple normal crossing divisor at t=0. What is the dual variety in the limit? We answer this question for a hypersurface of degree d degenerate to the union of two hypersurfaces of degree d_1 and d-d_1 meeting transversely. We find all the irreducible components of the dual variety in the limit and their multiplicities.

preprint2023arXivOpen access
Yilong Zhang
math.AG
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Yilong Zhang

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