论文标题
PICARD数字1与组成代数相关的PICARD 1号射击对称流形的刚度
Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras
论文作者
论文摘要
对于每个复杂组成代数$ \ mathbb {a} $，Picard第一的投影对称歧管$ x（\ Mathbb {a}）$ of Picard数字，这只是以下品种$ {\ rm lag}（\ rm lag}（\ rm lag}（3,6），{\ rm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm grm e_7/p_7。$在本文中，事实证明，这些品种是刚性的，即，如果一个纤维是$ x（\ m athbb {a}）$同构的任何光滑的投射歧管，那么每个纤维都是同X（\ Mathbb {a}）$，那么每个纤维都是同型至$ x（\ x（\ mathbb {\ mathbb {a a} a} a}）$。
To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties ${\rm Lag}(3,6), {\rm Gr}(3,6), \mathbb{S}_6, E_7/P_7.$ In this paper, it is proven that these varieties are rigid, namely for any smooth family of projective manifolds over a connected base, if one fiber is isomorphic to $X(\mathbb{A})$, then every fiber is isomorphic to $X(\mathbb{A})$.
