Star points on smooth hypersurfaces
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- 作者：Filip Cools ; Marc Coppens
- 关键词：Star points ; Smooth hypersurfaces
- 刊名：Journal of Algebra
- 出版年：2010
- 出版时间：1 January 2010
- 年：2010
- 卷：323
- 期：1
- 页码：261-286
- 全文大小：461 K
文摘
A point P on a smooth hypersurface X of degree d in is called a star point if and only if the intersection of X with the embedded tangent space TP(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 . 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.