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

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.

Keywords

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

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Peking University