Singularities of generic projection hypersurfaces

Doherty, Davis

doi:10.1090/S0002-9939-08-09286-1

Singularities of generic projection hypersurfaces
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Proc. Amer. Math. Soc. 136 (2008), 2407-2415 Request permission

Abstract:

Linearly projecting smooth projective varieties provide a method of obtaining hypersurfaces birational to the original varieties. We show that in low dimension, the resulting hypersurfaces only have Du Bois singularities. Moreover, we conclude that these Du Bois singularities are in fact semi log canonical. However, we demonstrate the existence of counterexamples in high dimension – the generic linear projection of certain varieties of dimension 30 or higher is neither semi log canonical nor Du Bois.

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