$F$-SIGNATURE UNDER BIRATIONAL MORPHISMS. (17th April 2019) - MA, LINQUAN; POLSTRA, THOMAS; SCHWEDE, KARL; TUCKER, KEVIN
Abstract : We study $F$ -signature under proper birational morphisms $\unicode[STIX]{x1D70B}:Y→ X$, showing that $F$ -signature strictly increases for small morphisms or if $K_{Y}\leqslant \unicode[STIX]{x1D70B}^{* }K_{X}$ . 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.