论文标题
原始形式没有更高的残留结构和可集成的层次结构（i）
Primitive Forms without Higher Residue Structure and Integrable Hierarchies (I)
论文作者
论文摘要
我们引入具有或没有更高残留结构的原始形式，并探索它们与具有KDV类型的度量且可集成的层次结构的平坦结构的联系。就像具有度量arxiv的原始形式的经典案例：1311.1659一样，无指标的原始形式也被构建为相对于下降变量的正式振荡积分的伯克霍夫分解的积极部分。原始形式的振荡积分没有度量产生kDV类型的通勤PDE的层次结构，就像用度量的原始形式一样。这应在（ii）中进行研究。
We introduce primitive forms with or without higher residue structure and explore their connection with the flat structures with or without a metric and integrable hierarchies of KdV type. Just as the classical case of primitive forms with metric arXiv:1311.1659, the primitive forms without metrics are constructed as the positive part of the Birkhoff decomposition of formal oscillatory integrals with respect to the descendent variable. The oscilating integrals of a primitive form without metric give rise to a hierarchy of commuting PDE of the KdV type as in the case of primitive forms with metric. This shall be studied in (II).
