Some Results on Secant Varieties Leading to a Geometric Flip Construction
Some Results on Secant Varieties Leading to a Geometric Flip Construction
复制标题
导致几何翻转结构的割线品种的一些结果
作者：
P. Vermeire
我们研究了定义射影变量的方程与它的割线变量的性质之间的关系。特别地，我们利用定义方程间的协同信息来推导关于SecX的光滑性和正态性陈述，也得到了关于沿x变化的投影空间上的线性系统的信息。我们利用这些结果来几何构造，对于任意维的变化，首先由M. Thaddeus通过几何不变理论在曲线的情况下描述的翻转。
We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality statements about SecX and also to obtain information about linear systems on the blow up of projective space along a variety X. We use these results to geometrically construct, for varieties of arbitrary dimension, a flip first described in the case of curves by M. Thaddeus via Geometric Invariant Theory.