Projective Varieties with Cones as Tangential Sections - NZJM

New Zealand Journal of Mathematics

E. BallicoDept. of MathematicsUniversity of Trento38050 Povo (TN)ITALY$$¹ 

关键词: Tangent space;    cone;    quadric hypersurface;    strange curve;    strange variety;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

Let n be an integral non-degeneratem-dimensional variety defined over an algebraically closed field. Assume the existence of a non-empty open subset U of Xreg such that TPis an (m − 1)-dimensional cone with vertex containing P. Here we prove that either X is a quadric hypersurface or char() = p > 0, n = m + 1, deg(X) = pe for someand there is a codimension two linear subspace n such thatfor every . We also give an "explicit" description (in terms of polynomial equations) of all examples arisingin the latter case; dim(Sing(X)) = (m − 1) for every such X.

【 授权许可】

Unknown