论文标题
高度配对在较高的周期和混合霍奇结构上
Height Pairing on Higher Cycles and Mixed Hodge Structures
论文作者
论文摘要
为了获得光滑，投射的复杂品种，我们引入了与较高代数周期相关的几种混合霍奇结构。最值得注意的是，我们引入了一个混合的Hodge结构，用于一对较高的循环，该循环在精制的归一化络合物中并正确相交。在特殊情况下，这种混合的Hodge结构是定向的双重结构，其高度与前两位作者在上一篇论文中引入的较高的Archimedean高度配对一致。我们还计算了Bloch-Wigner Diologarithm函数给出的该高度的非平凡示例。最后，我们研究了Hodge-Tate类型的混合Hodge结构的变化，并表明高度连续延伸至退化情况。
For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized complex and intersect properly. In a special case, this mixed Hodge structure is an oriented biextension, and its height agrees with the higher archimedean height pairing introduced in a previous paper by the first two authors. We also compute a non-trivial example of this height given by Bloch-Wigner dilogarithm function. Finally we study the variation of mixed Hodge structures of Hodge-Tate type, and show that the height extends continuously to degenerate situations.
