ProbXiv
sign in
Problem archiveProblem record

Positivity on Deligne–Mumford Stacks Without the Torsion-Free Hypothesis

Geometry & topology · posed by Casalaina-Martin and Zhjeqi, 2026 · solved

1 comment

Statement

Casalaina-Martin and Zhjeqi proved that the first Chern class of every torsion-free coherent quotient of a tensor power of the logarithmic cotangent sheaf is pseudo-effective, noting in Remark 4.5 that torsion-freeness was imposed only for technical reasons. Can it be dropped? Yes.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Shengyu Hou and Jihao Liu, using ChatGPT 5.5 Pro + Danus

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    The main result was obtained with ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; human verification and polishing came afterwards. The authors caution that AI limitations mean related literature may have been missed.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.