TY - JOUR
T1 - On the canonical bundle formula and log abundance in positive characteristic
AU - Witaszek, Jakub
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field k of characteristic p> 5 , which in turn implies the termination of any sequence of three-dimensional flips in the pseudo-effective case. We also show the log abundance conjecture for threefolds over k when the nef dimension is not maximal, and the base point free theorem for threefolds over F¯ p when p> 2.
AB - We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing conjecture for three-dimensional klt pairs over any algebraically closed field k of characteristic p> 5 , which in turn implies the termination of any sequence of three-dimensional flips in the pseudo-effective case. We also show the log abundance conjecture for threefolds over k when the nef dimension is not maximal, and the base point free theorem for threefolds over F¯ p when p> 2.
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U2 - 10.1007/s00208-021-02231-5
DO - 10.1007/s00208-021-02231-5
M3 - Article
AN - SCOPUS:85109699204
SN - 0025-5831
VL - 381
SP - 1309
EP - 1344
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -