Projective Varieties with Cones as Tangential Sections - NZJM

摘要

Let n be an integral non-degenerate m-dimensional variety defined over an algebraically closed field . Assume the existence of a non-empty open subset U of Xreg such that TP is 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 some and there is a codimension two linear subspace n such that for every . We also give an "explicit" description (in terms of polynomial equations) of all examples arising in the latter case; dim(Sing(X)) = (m − 1) for every such X.