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geometry-topology / Algebraic Geometry, Stacks

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

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.

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geometry-topologyJul 29, 2026Significance 5/100Registry: unreviewed

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

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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.

Source authenticatedPositivity on Deligne–Mumford Stacks Without the Torsion-Free Hypothesis →
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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.

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