Pith. sign in

REVIEW 4 cited by

Nakai-Moishezon criterions for complex Hessian equations

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2012.07956 v1 pith:GXR3EWZS submitted 2020-12-14 math.DG math.AGmath.AP

Jian Song This is my paper · ORCID
classification math.DGmath.AGmath.AP
keywords ahlerequationcriterionnakai-moishezoncomplexconditionconjectureequivalent
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

The $J$-equation proposed by Donaldson is a complex Hessian quotient equation on K\"ahler manifolds. The solvability of the $J$-equation is proved by Song-Weinkove to be equivalent to the existence of a subsolution. It is also conjectured by Lejmi-Szekelyhidi to be equivalent to a stability condition in terms of holomorphic intersection numbers as an analogue of the Nakai-Moishezon criterion in algebraic geometry. The conjecture is recently proved by Chen under a stronger uniform stability condition. In this paper, we establish a Nakai-Moishezon type criterion for pairs of K\"ahler classes on analytic K\"ahler varieties. As a consequence, we prove Lejmi-Szekelyhidi's original conjecture for the $J$-equation. We also apply such a criterion to obtain a family of constant scalar curvature K\"ahler metrics on smooth minimal models.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. A numerical criterion for complex Hessian type equations on projective manifolds

    math.DG 2026-08 conditional novelty 7.0 of 10

    Existence of solutions to complex Hessian-type equations on projective manifolds is equivalent to uniform positivity of certain subvariety integrals when the associated polynomial is strictly right-Noetherian.

  2. On the Datar-Mete-Song minimal slope conjecture

    math.AG 2026-08 conditional novelty 7.0 of 10

    The paper proves the Datar-Mete-Song conjecture: a pair of Kähler classes is semi-stable exactly when its minimal J-slope equals the topological J-slope.

  3. The deformed Vortex equations and equivariant stability conditions

    math.DG 2026-07 conditional novelty 7.0 of 10

    On vortex-type SU(2)-equivariant bundles over a product of a curve with P¹, solvability of the deformed Hermitian–Yang–Mills system is equivalent to Z-stability, and Bridgeland stability implies Z-stability.

  4. Ideal G{\aa}rding polynomials

    math.CO 2026-07 conditional novelty 7.0 of 10

    Ideal Gårding polynomials — a convexity-enhanced subclass of Gårding polynomials — are characterized by concavity and Lorentzian conditions, and univariate members are modeled by Pitman–Stanley polytope volumes.

Pith tools