Singularities of generic projection hypersurfaces

Details Singularities of generic projection hypersurfaces Singularities of generic projection hypersurfaces

2007-05-30

arxiv.org/abs/0705.4481v2

Mathematics

Algebraic Geometry

9 pages; Proof of Theorem 4.2 updated; Corollary 4.4 clarified

Scientific paper

Linearly projecting smooth projective varieties provides 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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