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On the Minimal Model Program for K\"ahler 3-folds

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arxiv 2306.11708 v2 pith:37USYYBR submitted 2023-06-20 math.AG math.CV

Omprokash Das , Christopher Hacon This is my paper · ORCID
classification math.AGmath.CV
keywords dimensionminimalahlercontractionsdivisorialexistenceflipsmodel
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abstract

In this article we prove the existence of pl-flipping and divisorial contractions and pl flips in dimension $n$ for compact K\"ahler varieties, assuming results of the minimal model program in dimension $n-1$. We also give a self contained proof of the cone theorem, the existence of flipping and divisorial contractions, of flips and minimal models in dimension 3.

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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. On the K\"ahler MMP and the transcendental base-point-free theorem

    math.AG 2026-07 accept novelty 7.0 of 10

    Big gklt Kähler pairs admit a full MMP with scaling, and a nef canonical class with modified-big boundary is semiample (Tosatti’s conjecture).

  2. The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors

    math.AG 2025-07 conditional novelty 7.0 of 10

    For projective klt varieties with big canonical or anticanonical divisor, the Miyaoka-Yau Chern class inequality holds when intersections are taken with the non-pluripolar product.

  3. Semipositivity of the orbifold second Chern class in Fujiki's class

    math.AG 2026-07 conditional novelty 6.0 of 10

    For compact normal analytic varieties in Fujiki's class, Miyaoka's inequality holds when the canonical divisor is nef, and the orbifold second Chern class is semipositive when the anti-canonical divisor is nef, under ...

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