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Variation of the Variety of Minimal Rational Tangents of Cyclic Coverings
Published online by Cambridge University Press: 28 August 2018
Abstract
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.
MSC classification
Primary:
14J45: Fano varieties
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 115 - 123
- Copyright
- Copyright © Edinburgh Mathematical Society 2018
References
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