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Analytical findings reveal that if one sequence of flips terminates in pseudoeffective projective pairs, it suggests all flips may terminate, supporting a Nakayama-Zariski conjecture.
We show that for pseudoeffective projective pairs the termination of one sequence of flips implies the termination of all flips, assuming a natural conjecture on the behaviour of the Nakayama-Zariski decomposition under the operations of a Minimal Model Program.
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Lazic et al. (2025) studied this question.
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