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arXiv · 2312.17728

Degeneration of Dual Varieties of Hypersurfaces

Yilong Zhang
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Abstract

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.

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Yilong Zhang. 2023-12-29. Degeneration of Dual Varieties of Hypersurfaces. https://arxiv.org/abs/2312.17728

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