PreprintCC BY 4.0arXiv
Kawamata-Viehweg and Lipman's vanishings for sequences of blow-ups at regular closed points
Abstract
The birational Kawamata-Viehweg vanishing theorem (KVV for short) is known to hold in considerable generality in equal characteristic zero, but fails in general in positive characteristic. We study a vanishing conjecture of Lipman for sequences of blow-ups at closed points of the spectrum of a regular local ring. We prove the conjecture when the ring has dimension at most three. We also establish a relative Kawamata-Viehweg vanishing theorem for exceptional nef Q-divisors when all blow-up centers are rational over the residue field and the positive residue characteristic is at least the dimension of the ring minus one. Both results allow mixed characteristic.
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BibTeX
@misc{ishii2026kawamataviehweg,
title = {{Kawamata-Viehweg and Lipman's vanishings for sequences of blow-ups at regular closed points}},
author = {Shihoko Ishii},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26518},
eprint = {2610.26518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26518},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kawamata-Viehweg and Lipman's vanishings for sequences of blow-ups at regular closed points
AU - Shihoko Ishii
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26518
UR - https://arxiv.org/abs/2610.26518
AB - The birational Kawamata-Viehweg vanishing theorem (KVV for short) is known to hold in considerable generality in equal characteristic zero, but fails in general in positive characteristic. We study a vanishing conjecture of Lipman for sequences of blow-ups at closed points of the spectrum of a regular local ring. We prove the conjecture when the ring has dimension at most three. We also establish a relative Kawamata-Viehweg vanishing theorem for exceptional nef Q-divisors when all blow-up centers are rational over the residue field and the positive residue characteristic is at least the dimension of the ring minus one. Both results allow mixed characteristic.
ER -