Positivity of logarithmic cotangent quotients on Deligne–Mumford stacks

Under the cited smooth proper integral complex Deligne–Mumford stack, normal-crossings divisor and big-determinant subsheaf hypotheses, is the first Chern class of every coherent quotient of every positive tensor power of the logarithmic cotangent sheaf pseudo-effective?

Why it matters and what counts as progress

Why it matters: Including torsion quotients closes a gap left by the known torsion-free quotient theorem.

What counts as progress: A positivity proof for arbitrary coherent quotients under those hypotheses, or a quotient showing the torsion extension fails.

How the problem developed

May 2026 · Partial result [1]
Sebastian Casalaina-Martin and Shend Zhjeqi Published related positivity results for logarithmic geometry on Deligne–Mumford stacks; the cited research record identifies their earlier quotient result as limited to torsion-free quotients.
29 Jul 2026 · Theorem [2]
Hou and Liu Released a proof claiming pseudo-effectivity for coherent quotients, including torsion quotients, under smoothness, properness, integral-stack, normal-crossings and determinant hypotheses.

AI contribution

Removing the Torsion-free Hypothesis in a Positivity Theorem on Deligne-Mumford Stacks

Shengyu Hou, Jihao Liu

Hou and Liu prove pseudo-effectivity of the first Chern class for every coherent quotient of every positive tensor power of the logarithmic cotangent sheaf under their smooth proper integral complex Deligne–Mumford stack, normal-crossings divisor, and big-determinant subsheaf hypotheses.

AI involvementAI-centered

ImportanceModest

Technical verificationFormal (human)

Human understandingFull