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cyclic covering

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Variation of the Variety of Minimal Rational Tangents of Cyclic Coverings
Part of
- Surfaces and higher-dimensional varieties
Hosung Kim
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 1 / February 2019

Published online by Cambridge University Press:

28 August 2018, pp. 115-123
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Let π: X → ℙn be the d-cyclic covering branched along a smooth hypersurface Y ⊂ ℙn of degree d, 3 ≤ d ≤ n. We identify the minimal rational curves on X with d-tangent lines of Y and describe the scheme structure of the variety of minimal rational tangents 𝒞x ⊂ ℙTx(X) at a general point x ∈ X. We also show that the projective isomorphism type of 𝒞x varies in a maximal way as x moves over general points of X.