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论文类型：期刊论文

发表时间：2014-11-01

发表刊物：SCIENCE CHINA-MATHEMATICS

收录刊物：SCIE

卷号：57

期号：11

页面范围：2273-2284

ISSN号：1674-7283

关键字：characteristic number; algebraic hypersurfaces; Pascal's theorem; characteristic mapping; simplex

摘要：Projective invariants are not only important objects in mathematics especially in geometry, but also widely used in many practical applications such as in computer vision and object recognition. In this work, we show a projective invariant named as characteristic number, from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property, two high-dimensional generalizations of Pascal's theorem are given, one establishing the connection of hypersurfaces of distinct degrees, and the other concerned with the intersections of a hypersurface and a simplex.