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Remarks on the abundance conjecture

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arxiv 1509.04626 v2 pith:F3TRMKLG submitted 2015-09-15 math.AG

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classification math.AG
keywords abundancecanonicalfoldsconjectureassumingboundarydiscussdivisor
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abstract

We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.

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Cited by 2 Pith papers

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  1. Minimal model program for normal pairs along log canonical locus in complex analytic setting

    math.AG 2025-01 conditional novelty 6.0 of 10

    The complex analytic analog of the minimal model program for normal pairs along the log canonical locus holds: under a semi-ampleness hypothesis on the non-lc locus, an MMP sequence exists and terminates at a good min...

  2. Addendum: On generalized canonical bundle formula and boundedness of complements in complex analytic setting

    math.AG 2026-06 unverdicted novelty 4.0 of 10

    Proves generalized canonical bundle formula for lc-trivial fibrations without nef part assumption in complex analytic setting, plus algebraic counterpart.

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