PreprintCC BY 4.0arXiv
Log canonical models of a fixed variety with varying boundaries
Abstract
Motivated by extending the Morrison-Kawamata cone conjecture beyond Calabi-Yau varieties and Severi-Maehara type finiteness results to targets not necessarily of general type, we fix a smooth projective variety and study the finiteness of its log canonical models as klt boundaries vary. Our main result establishes finiteness for every smooth projective minimal surface. For each κ∈{−∞,0,1}, we construct a smooth projective non-minimal surface of Kodaira dimension κ with infinitely many log canonical models, showing that the minimality assumption cannot be omitted in general. We also investigate possible extensions of this finiteness result to higher dimensions.
Related
- A Time-Varying Coefficient-Based Fixed-Time Neurodynamic Approach for Generalized Monotone Inclusion Problems and Its Applications
- Comparing SGLD and a fixed-noise predictor-corrector adaptation in canonical joint energy-based models on CIFAR-10
- A priori bounds for geodesic diameter. Part III. A Sobolev–Poincaré inequality and applications to a variety of geometric variational problems
- The variety generated by all additively idempotent semirings of order four
- The number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety
BibTeX
@misc{li2026canonical,
title = {{Log canonical models of a fixed variety with varying boundaries}},
author = {Xingying Li and Zhan Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03305},
eprint = {2609.03305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Log canonical models of a fixed variety with varying boundaries
AU - Xingying Li
AU - Zhan Li
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.03305
UR - https://arxiv.org/abs/2609.03305
AB - Motivated by extending the Morrison-Kawamata cone conjecture beyond Calabi-Yau varieties and Severi-Maehara type finiteness results to targets not necessarily of general type, we fix a smooth projective variety and study the finiteness of its log canonical models as klt boundaries vary. Our main result establishes finiteness for every smooth projective minimal surface. For each κ∈{−∞,0,1}, we construct a smooth projective non-minimal surface of Kodaira dimension κ with infinitely many log canonical models, showing that the minimality assumption cannot be omitted in general. We also investigate possible extensions of this finiteness result to higher dimensions.
ER -