Abstract
Let f : ( X, x) → ( C, 0) be a smoothing. We show that the Lefschetz number of the monodromy Λ ( f) depends only on data provided by some resolution of space ( X, x) and the pull-back of f. Moreover, we prove that Λ ( f) depends only on the residue class of f modulo the intersection of certain ideals which are uniquely defined by the underlying space; this will be a consequence of a more general statement about uniqueness of minimal filtrations defined by exceptional divisors.
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