Computing jumping numbers in higher dimensions

The aim of this paper is to generalize the algorithm to compute jumping numbers on rational surfaces described in Alberich-Carramiñana et al. (Mich Math J 65(2):287320, 2016) to varieties of dimension at least 3. Therefore, we introduce the notion of \(\pi \)-antieffective divisors, generalizing antinef divisors. Using these divisors, we present a way to find a small subset of the ‘classical’ candidate jumping numbers of an ideal, containing all the jumping numbers. Moreover, many of these numbers are automatically jumping numbers, and in many other cases, it can be easily checked.