This research computes the F-signature in ruled surfaces, revealing differing singularities in prime characteristic rings.
We compute the ‐signature function of the ample cone of any nontrivial ruled surface over , where is an algebraically closed field of prime characteristic. As an application, we construct a Noetherian ‐finite strongly ‐regular ring of prime characteristic admitting two maximal ideals at which the Hilbert–Kunz multiplicity and ‐signature measure different singularities; that is, and . Our calculation of the a preprint by other authors.
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Lee et al. (2026) studied this question.