Geodesic
$F$-SIGNATURE UNDER BIRATIONAL MORPHISMS
Forum of Mathematics, Sigma, Tome 7 (2019)

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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. 
@article{10_1017_fms_2019_6,
     author = {LINQUAN MA and THOMAS POLSTRA and KARL SCHWEDE and KEVIN TUCKER},
     title = {$F${-SIGNATURE} {UNDER} {BIRATIONAL} {MORPHISMS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {7},
     year = {2019},
     doi = {10.1017/fms.2019.6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.6/}
}
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LINQUAN MA; THOMAS POLSTRA; KARL SCHWEDE; KEVIN TUCKER. $F$-SIGNATURE UNDER BIRATIONAL MORPHISMS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.6

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