Year: 2019
Type: article
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.
Source: Forum of Mathematics Sigma
DOI: 10.1017/fms.2019.6
Authors: LINQUAN MA, THOMAS POLSTRA, KARL SCHWEDE, KEVIN TUCKER
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,000
Awards: Analytic Methods in Complex Algebraic Geometry, G1689101714, Studies in Commutative Algebra, CAREER: Test Ideals and the Geometry of Projective Varieties in Positive Characteristic, G4589787539, Studies in Commutative Algebra, Commutative Algebra: Singularities in All Characteristics with Geometric Applications, G6000716047, G6671297155, PostDoctoral Research Fellowship, Computing and Interpreting Frobenius Invariants, CAREER: Test Ideals and the Geometry of Projective Varieties in Positive Characteristic
OpenAlex ID: W2894066235