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- W2165440894 abstract "Let $$phi : X rightarrow mathbb{P }^n$$ be a double cover branched along a smooth hypersurface of degree $$2m, 2 le m le n-1$$ . We study the varieties of minimal rational tangents $$mathcal{C }_x subset mathbb{P }T_x(X)$$ at a general point $$x$$ of $$X$$ . We describe the homogeneous ideal of $$mathcal{C }_x$$ and show that the projective isomorphism type of $$mathcal{C }_x$$ varies in a maximal way as $$x$$ varies over general points of $$X$$ . Our description of the ideal of $$mathcal{C }_x$$ implies a certain rigidity property of the covering morphism $$phi $$ . As an application of this rigidity, we show that any finite morphism between such double covers with $$m=n-1$$ must be an isomorphism. We also prove that Liouville-type extension property holds with respect to minimal rational curves on $$X$$ ." @default.
- W2165440894 created "2016-06-24" @default.
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- W2165440894 date "2012-12-09" @default.
- W2165440894 modified "2023-10-16" @default.
- W2165440894 title "Varieties of minimal rational tangents on double covers of projective space" @default.
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- W2165440894 doi "https://doi.org/10.1007/s00209-012-1125-6" @default.
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