论文标题
特征两个的立方表面
Cubic Surfaces of Characteristic Two
论文作者
论文摘要
从主要特征交换代数的角度研究了特征两个中的立方表面。特别是，我们证明，非佛罗里赛分裂的立方体表面在所有立方体的19维空间中形成了编成四分之一的线性子空间，并且直到投影等效性，都有许多非果皮分裂表面有限的。我们明确描述了每个方程的定义方程，并将其表征为极端的线条，从线上的线上构型来描述。特别是，特征中的（可能是奇异的）立方表面在且仅当其上没有三行形成“三角形”时，就无法分裂。
Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that, the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the 19-dimensional space of all cubics, and that up to projective equivalence, there are finitely many non-Frobenius split cubic surfaces. We explicitly describe defining equations for each and characterize them as extremal in terms of configurations of lines on them. In particular, a (possibly singular) cubic surface in characteristic two fails to be Frobenius split if and only if no three lines on it form a "triangle".
