Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and ...Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]＋1 dimensional quadrics passing through one point.展开更多
文摘Let X C P^NC be an n-dimensional nondegenerate smooth projective variety containing an mdimensional subvariety Y.Assume that either m〉n/2 and X is a complete intersection or that m≥ N2.We show deg（X）｜deg（Y）and codim Y Y ≥codimPN X,where Y is the linear span of Y.These bounds are sharp.As an application,we classify smooth projective n-dimensional quadratic varieties swept out by m≥[n/2]＋1 dimensional quadrics passing through one point.
