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We investigate some necessary and sufficient conditions for an exceptionaldivisor to contribute jumping numbers of an effective divisor on a variety ofarbitrary dimension, inspired by the results for curves on surfaces by Smithand Thompson and Tucker. In particular, we construct an example of anexceptional divisor that is not contracted in the log canonical model, and doesnot contribute any jumping numbers.

Contribution of jumping numbers by exceptional divisors, with an appendix by Karen E. Smith and Kevin Tucker