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PreprintCC BY 4.0arXiv

Coupled Pklt Tuples and Varieties of Pklt Type

  • Donghyeon Kim
  • Dae-Won Lee
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Abstract

We introduce asymptotic multiplier ideal sheaves and log canonical thresholds associated with tuples of pseudoeffective divisors on a projective klt pair. We prove that the threshold of a coupled potentially klt tuple is computed by a quasi-monomial valuation. For varieties of potentially klt type, we prove that every big divisor admits a birational Zariski decomposition with semiample positive part. We also prove finite generation of multisection rings of big divisors and give a criterion for a variety of potentially klt type to be a Mori dream space.

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Cite

BibTeXRIS
BibTeX
@misc{kim2026coupled,
  title = {{Coupled Pklt Tuples and Varieties of Pklt Type}},
  author = {Donghyeon Kim and Dae-Won Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11107},
  eprint = {2609.11107},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11107},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Coupled Pklt Tuples and Varieties of Pklt Type
AU  - Donghyeon Kim
AU  - Dae-Won Lee
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11107
UR  - https://arxiv.org/abs/2609.11107
AB  - We introduce asymptotic multiplier ideal sheaves and log canonical thresholds associated with tuples of pseudoeffective divisors on a projective klt pair. We prove that the threshold of a coupled potentially klt tuple is computed by a quasi-monomial valuation. For varieties of potentially klt type, we prove that every big divisor admits a birational Zariski decomposition with semiample positive part. We also prove finite generation of multisection rings of big divisors and give a criterion for a variety of potentially klt type to be a Mori dream space.
ER  -