TY - JOUR

T1 - Stability of test ideals of divisors with small multiplicity

AU - Sato, Kenta

N1 - Funding Information:
Acknowledgements The author wishes to express his gratitude to his supervisor Professor Shunsuke Takagi for his encouragement, valuable advice and suggestions. He is grateful to Doctor Sho Ejiri for his encouragement. He is also grateful to an anonymous referee for many useful suggestions and for pointing out many typos. This work was supported by the Program for Leading Graduate Schools, MEXT, Japan.
Publisher Copyright:
© 2017, Springer-Verlag GmbH Deutschland.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Let (X, Δ) be a log pair in characteristic p> 0 and P be a (not necessarily closed) point of X. We show that there exists a constant δ> 0 such that the test ideal τ(X, Δ) , a characteristic p analogue of a multiplier ideal, does not change at P under the perturbation of Δ by any R-divisor with multiplicity less than δ. As an application, we prove that if D is an R-Cartier R-divisor on a strongly F-regular projective variety, then the non-nef locus of D coincides with the restricted base locus of D. This is a generalization of a result of Mustaţǎ to the singular case and can be viewed as a characteristic p analogue of a result of Cacciola–Di Biagio.

AB - Let (X, Δ) be a log pair in characteristic p> 0 and P be a (not necessarily closed) point of X. We show that there exists a constant δ> 0 such that the test ideal τ(X, Δ) , a characteristic p analogue of a multiplier ideal, does not change at P under the perturbation of Δ by any R-divisor with multiplicity less than δ. As an application, we prove that if D is an R-Cartier R-divisor on a strongly F-regular projective variety, then the non-nef locus of D coincides with the restricted base locus of D. This is a generalization of a result of Mustaţǎ to the singular case and can be viewed as a characteristic p analogue of a result of Cacciola–Di Biagio.

UR - http://www.scopus.com/inward/record.url?scp=85028588720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028588720&partnerID=8YFLogxK

U2 - 10.1007/s00209-017-1913-0

DO - 10.1007/s00209-017-1913-0

M3 - Article

AN - SCOPUS:85028588720

SN - 0025-5874

VL - 288

SP - 783

EP - 802

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -