Hodge theory of degenerations, (I): Consequences of the decomposition theorem

Abstract

We use the Decomposition Theorem to derive several generalizations of the Clemens-Schmid sequence, relating asymptotic Hodge theory of a degeneration to the mixed Hodge theory of its singular fiber(s).

53 pages; final version, to appear in Selecta Math.; Appendix by Morihiko Saito discussing the equivalence between Decomposition theorem over Stein curves and the Clemens--Schmid exact sequence