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Variation of the Variety of Minimal Rational Tangents of Cyclic Coverings

Published online by Cambridge University Press:  28 August 2018

Hosung Kim*
Affiliation:
Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, Republic of Korea (hosung@kias.re.kr)

Abstract

Let π: X → ℙn be the d-cyclic covering branched along a smooth hypersurface Y ⊂ ℙn of degree d, 3 ≤ dn. 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 xX. 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

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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