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TITLE VARIATION OF THE VARIETY OF MINIMAL RATIONAL TANGENTS OF CYCLIC COVERINGS
KIAS AUTHORS Kim, Hosung
JOURNAL PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2019
ARCHIVE  
ABSTRACT Let pi : X -> P-n be the d-cyclic covering branched along a smooth hypersurface Y subset of P-n 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 C-x subset of PTx(X) at a general point x is an element of X. We also show that the projective isomorphism type of C-x varies in a maximal way as x moves over general points of X.
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