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Award ID contains: 1703856

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  1. ; (, Michigan Mathematical Journal)
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  2. ; ; ; ; (, Journal of Singularities)
    null (Ed.)
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  3. ; (, Nagoya Mathematical Journal)
    We establish the continuity of Hilbert–Kunz multiplicity and F-signature as functions from a Cohen–Macaulay local ring $$(R,\mathfrak{m},k)$$ of prime characteristic to the real numbers at reduced parameter elements with respect to the $$\mathfrak{m}$$ -adic topology. 
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  4. ; (, Journal of Algebra)
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  5. ; ; ; (, Forum of Mathematics, Sigma)
    We study $$F$$ -signature under proper birational morphisms $$\unicode[STIX]{x1D70B}:Y\rightarrow X$$ , showing that $$F$$ -signature strictly increases for small morphisms or if $$K_{Y}\leqslant \unicode[STIX]{x1D70B}^{\ast }K_{X}$$ . In certain cases, we can even show that the $$F$$ -signature of $$Y$$ is at least twice as that of  $$X$$ . We also provide examples of $$F$$ -signature dropping and Hilbert–Kunz multiplicity increasing under birational maps without these hypotheses. 
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