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Exponents of an irreducible plane curve singularity
Morihiko Saito
We give an explicit formula for the exponents (i.e. the spectra up to the shift by one) of an irreducible plane curve singularity in terms of Puiseux pairs. As an application we pr…
Monodromy Filtration and Positivity
Morihiko Saito
We study Deligne's conjecture on the monodromy weight filtration on the nearby cycles in the mixed characteristic case, and reduce it to the nondegeneracy of certain pairings in th…
Bloch's Conjecture and Chow Motives
Morihiko Saito
Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homological…
Monodromy at Infinity and the Weights of Cohomology
Alexandru Dimca, Morihiko Saito
We show that for a polynomial map, the size of the Jordan blocks for the eigenvalue 1 of the monodromy at infinity is bounded by the multiplicity of the reduced divisor at infinity…