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We prove formulas for the number of Jordan blocks of the maximal size forlocal monodromies of one-parameter degenerations of complex algebraic varietieswhere the bound of the size comes from the monodromy theorem. In case thegeneral fibers are smooth and compact, the proof calculates some part of theweight spectral sequence of the limit mixed Hodge structure of Steenbrink. Inthe singular case, we can prove a similar formula for the monodromy on thecohomology with compact supports, but not on the usual cohomology. We also showthat the number can really depend on the position of singular points in theembedded resolution even in the isolated singularity case, and hence there areno simple combinatorial formulas using the embedded resolution in general.

Number of Jordan blocks of the maximal size for local monodromies