On Generalized Lc Pairs with b-log Abundant Nef Part (with an Appendix by J. Han)

Junpeng Jiao; Jihao Liu; Lingyao Xie

doi:10.1007/s11464-025-0033-0

Frontiers of Mathematics ›› : 1 -31. DOI: 10.1007/s11464-025-0033-0

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On Generalized Lc Pairs with b-log Abundant Nef Part (with an Appendix by J. Han)

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Abstract

We study the behavior of NQC generalized lc pairs with b-log abundant nef part. We show that this structure is preserved under the canonical bundle formula and sub-adjunction formulas, and is also compatible with the non-vanishing conjecture and the abundance conjecture in the classical minimal model program. As an application, we prove the non-vanishing theorem for rationally connected log canonical pairs, improving a result of Gongyo.

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Canonical bundle formula / moduli b-divisor / non-vanishing / 14E30 / 14C20 / 14E05 / 14J17

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Junpeng Jiao, Jihao Liu, Lingyao Xie. On Generalized Lc Pairs with b-log Abundant Nef Part (with an Appendix by J. Han). Frontiers of Mathematics 1-31 DOI:10.1007/s11464-025-0033-0