Pith. sign in

REVIEW 3 cited by

Irreducible symplectic varieties with a large second Betti number

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 2410.01566 v5 pith:2USP5XMP submitted 2024-10-02 math.AG

Yuchen Liu , Zhiyu Liu , Chenyang Xu This is my paper · ORCID
classification math.AG
keywords irreduciblesymplecticbetticubicfibrationlagrangiannumbersecond
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian fibration of cubic fivefolds containing a fixed cubic fourfold can be compactified by a $\mathbb{Q}$-factorial terminal irreducible symplectic variety with the second Betti number at least 24, and admits a Lagrangian fibration whose base is a weighted projective space. In particular, it belongs to a new deformation type of irreducible symplectic varieties.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Boundedness of some fibered K-trivial varieties

    math.AG 2025-07 conditional novelty 8.0 of 10

    Fixed-dimension Calabi-Yau varieties with abelian or primitive symplectic fibrations are birationally bounded, and Lagrangian-fibered primitive symplectic varieties have finitely many deformation classes.

  2. Abelian fiber spaces and their Tate-Shafarevich twists with sections

    math.AG 2025-04 conditional novelty 7.0 of 10

    A construction produces a Tate-Shafarevich twist with a rational section from any suitably conditioned abelian fiber space.

  3. O'Grady's tenfolds from stable bundles on hyper-K\"ahler fourfolds

    math.AG 2024-11 conditional novelty 7.0 of 10

    A moduli-space construction realizes the Laza-Saccà-Voisin compactification and yields infinitely many new families of O'Grady's ten-dimensional hyper-Kähler manifolds.

Pith tools