Star points on smooth hypersurfaces

Details Star points on smooth hypersurfaces Star points on smooth hypersurfaces

2009-03-11

arxiv.org/abs/0903.2005v1

Mathematics

Algebraic Geometry

30 pages, 1 figure

Scientific paper

A point P on a smooth hypersurface X of degree d in an N-dimensional projective space is called a star point if and only if the intersection of X with the embedded tangent space T_P(X) is a cone with vertex P. This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in three-dimensional projective space. We generalize results on the configuration space of total inflection points on plane curves to star points. We give a detailed description of the configuration space for hypersurfaces with two or three star points. We investigate collinear star points and we prove that the number of star points on a smooth hypersurface is finite.

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