科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this note we prove the following surprising characterization: if X subset of A(n) is an (embedded, non-empty, proper) algebraic variety defined over a field k of characteristic zero, then X is a hypersurface if and only if the module TOAn/k (X) of logarithmic vector fields of X is a reflexive OA(n)-module. As a consequence of this result, we derive that if TOAn/k (X) is a free O-A(n)-module, which is shown to be equivalent to the freeness of the t-th exterior power of TOAn/k (X) for some (in fact, any) t < n, then necessarily X is a Saito free divisor.
- 出版日期2018-3
