Geometric properties of the double-point divisor

Ilic, Bo

doi:10.1090/S0002-9947-98-01928-X

Geometric properties of the double-point divisor
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by Bo Ilic

Trans. Amer. Math. Soc. 350 (1998), 1643-1661

DOI: https://doi.org/10.1090/S0002-9947-98-01928-X

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Abstract:

The locus of double points obtained by projecting a variety $X^{n} \subset \mathbf {P}^N$ to a hypersurface in $\mathbf {P}^{n+1}$ moves in a linear system which is shown to be ample if and only if $X$ is not an isomorphic projection of a Roth variety. Such Roth varieties are shown to exist, and some of their geometric properties are determined.

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