AI 中文总结
该研究针对射影簇，给出其线性自同构群维数的界，证明界可达当且仅当簇为欧拉对称簇，还确定了欧拉对称簇的无穷小自同构李代数并得到特化刚性结果。
AI 中文摘要
我们根据射影簇$Z \subset \mathbb{P} V$在一般点处的基本形式，给出其线性自同构群维数的一个界。此外，我们证明当且仅当$Z \subset \mathbb{P} V$射影等价于欧拉对称簇时，该界可达。作为副产品，我们确定了欧拉对称簇的无穷小自同构李代数，还得到了在保持基本形式同构类型的情况下欧拉对称簇的 specialization（特化）的刚性结果。
英文摘要
We give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset \mathbb{P} V$ in terms of its fundamental forms at a general point. Moreover, we show that the bound is achieved precisely when $Z \subset \mathbb{P} V$ is projectively equivalent to an Euler-symmetric variety. As a by-product, we determine the Lie algebra of infinitesimal automorphisms of an Euler-symmetric variety and also obtain a rigidity result on the specialization of an Euler-symmetric variety preserving the isomorphism type of the fundamental forms.
CommentsTo appear in Nagoya Mathematical Journal
