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Indexed by:期刊论文

Date of Publication:2014-11-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:57

Issue:11

Page Number:2273-2284

ISSN No.:1674-7283

Key Words:characteristic number; algebraic hypersurfaces; Pascal's theorem; characteristic mapping; simplex

Abstract: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.