关于不变基变换的注记

A Note on the Invariant─base─change

不变基变换在代数曲面的地理问题中有重要应用。本文给出具有不变基变换的奇异纤维的完全分类，并证明，当基变换的次数ｄ大于５时，具有不变基变换的奇异纤维是半稳定的；当ｄ≤５时，具有不变基变换的奇异纤维是既约的，并且最多只有简单曲线奇点。

The invariant─base─change has an important application in the geography of algebraic surfaces.In this paper,the classification of singular fibres having the invariant─base─change property is given.It is proven that if the degree d of the base change is larger than 5, then the singular fiber having the invariant─base─change property is semistable; if d≤5, then the singular fibre having the invariant─base─change property is reduced and has at most simple curve─singularities.