On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs

Abstract

We investigate the DCC property of the set of Iitaka volumes of a given set of pairs of varieties. We both generalize previous results of Birkar and Li about usual pairs to the real coefficient case, and also establish similar results on generalised pairs, where some natural boundedness assumptions are required for technical reasons.

40 pages; v2: added a new improved result in Section 5; the proof of Theorem 3.1 and Lemma 5.3 adapt the framework from arXiv:2311.12665, arXiv:2103.14935 with modifications to the present settings