On monodromies of a degeneration of irreducible symplectic Kähler manifolds

环面镜像单值群与拉格朗日球面

Toric mirror monodromies and Lagrangian spheres

该研究针对Gross-Siebert型环面退化中心纤维的同调镜像对称问题，证明Calabi-Yau情形下线丛在缠绕Fukaya范畴中的像可由拉格朗日球面表示，推进了同调镜像对称的具体几何对应研究。

Number of Jordan blocks of the maximal size for local monodromies

We prove formulas for the number of Jordan blocks of the maximal size for local monodromies of one-parameter degenerations of complex algebraic varieties where the bound of the size comes from the monodromy theorem. In case the general fibers are smooth and compact, the proof calculates some part of the weight spectral sequence of the limit mixed Hodge structure of Steenbrink. In the singular case, we can prove a similar formula for the monodromy on the cohomology with compact supports, but not on the usual cohomology. We also show that the number can really depend on the position of singular …