Pith. sign in

REVIEW 2 cited by

Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric

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 1607.03265 v1 pith:U6ISTHBT submitted 2016-07-12 math.CV math.AGmath.DG

Xu Wang This is my paper · ORCID
classification math.CVmath.AGmath.DG
keywords mathcalapplicationcriteriondirectimagemetricnegative-curvatureshall
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We shall show that $q$-semipositivity of the vector bundle $E$ over a K\"ahler total space $\mathcal X$ implies the Griffiths-semipositivity of the $q$-th direct image of $\mathcal O(K_{\mathcal X/B}\otimes E)$. As an application, we shall give a negative-curvature criterion for the generalized Weil-Petersson metric on the base manifold.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Curvature of the base manifold of a Monge-Amp\`ere fibration and its existence

    math.AG 2019-08 conditional novelty 6.0 of 10

    A Poisson-Kähler fibration has a canonical Kähler metric on its base whose holomorphic bisectional curvature is non-positive and whose holomorphic sectional, Ricci, and scalar curvatures are bounded above by a negativ...

  2. Bottom of the spectrum of complete noncompact K\"{a}hler manifolds

    math.DG 2026-06 unverdicted novelty 1.0 of 10

    Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.

Pith tools