$F$-SIGNATURE UNDER BIRATIONAL MORPHISMS. (17th April 2019)

• Record Type: Journal Article
• Authors: MA, LINQUAN; POLSTRA, THOMAS; SCHWEDE, KARL; TUCKER, KEVIN
• Is Part Of: Forum of mathematics. Volume 7(2019)
• Publication Date: 2019-04-17
• Subjects: 13A35, -- 14B05, -- 14C20; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2019.6
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract : 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.