On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs
Pinxian Bie
TL;DR
This paper studies the descending chain condition (DCC) property of Iitaka volumes for pairs of varieties with real coefficients and generalized pairs, extending previous results to broader contexts.
Contribution
It generalizes existing DCC results from usual pairs to real coefficient pairs and generalized pairs, under certain boundedness assumptions.
Findings
Established DCC property for Iitaka volumes of real coefficient pairs
Extended DCC results to generalized pairs with boundedness conditions
Generalized previous work by Birkar and Li to new settings
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.
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