Degeneration of log Hodge-de Rham spectral sequences and mixed Hodge structures

利用体元方法，构造了射影对数变形的相对log de Rham上同调群上的混合Hodge结构及其极化，并构造了多圆盘上的一个射影半稳定态射，这是对数光滑退化的一个典型例子.证明了当一般纤维的相对de Rham上同调群上的纯Hodge结构退化为多圆盘的某些坐标超平面的交时，极限混合Hodge结构给出了混合Hodge结构的一个容许变分.

By using cubical method, I constructed mixed Hodge structures and their polarizations on the relative log de Rham cohomology groups of a projective log deformation.On the other hand, I considerd a projective semistable morphism over a polydisc, which is a typical example of log smooth degeneration. I proved that the limiting mixed Hodge structures give us an admissible variation of mixed Hodge structures, when the pure Hodge structures on the relative de Rham cohomology groups of general fibers degenerate to an intersection of some of coordinate hyperplanes of the polydisc.