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Anticanonical divisor with good asymptotic base loci

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arxiv 2411.04628 v2 pith:WU4ETR72 submitted 2024-11-07 math.AG

Sung Rak Choi , Sungwook Jang , Dae-Won Lee This is my paper · ORCID
classification math.AG
keywords deltabasegoodasymptoticlociminimalanalogousanticanonical
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abstract

In this paper, we give a characterization of Fano type varieties in terms of the asymptotic base loci of $-(K_X+\Delta)$. We also show that for a potentially lc pair $(X,\Delta)$, if no plc centers are contained in the augmented base locus $\mathbf{B}_{+}(-(K_X+\Delta))$, then $(X,\Delta)$ has a good $-(K_X+\Delta)$-minimal model. This gives an analogous result of Birkar--Hu on the existence of good minimal models.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs

    math.AG 2025-01 conditional novelty 7.0 of 10

    A P-trivial MMP is introduced and used to show that several classes of generalised klt and lc pairs with Nakayama-Zariski decompositions have minimal models.

  2. K-stability of del Pezzo surfaces with a single quotient singularity

    math.AG 2025-07 conditional novelty 6.0 of 10

    K-stable del Pezzo surfaces with a single quotient singularity of type 1/(mn-1)(1,n) and two exceptional curves in the minimal resolution are exactly S^4_{2,2}, S^5_{2,2}, S^5_{3,2}, S^6_{3,2}, S^6_{4,2}, S^7_{4,2}, S...

  3. On minimal model program and Zariski decomposition of potential triples

    math.AG 2025-02 conditional novelty 5.0 of 10

    If the extra divisor in a potential triple admits a birational Zariski decomposition, the triple can be rewritten as a generalized pair, allowing the minimal model program to run.

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