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Variation of the Variety of Minimal Rational Tangents of Cyclic Coverings

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  28 August 2018

Hosung Kim
Hosung Kim*
Affiliation:
Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea ([email protected])
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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.

Keywords

cyclic coveringFano manifoldsvarieties of minimal rational tangents

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 

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References

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