PreprintCC BY 4.0arXiv
Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one
Abstract
Let f: M → ℂPn be a Lagrangian fibration on a compact hyperkahler manifold. We prove that f has no multiple fibers in codimension 1. We prove that this condition is equivalent to the primitivity of the fundamental class of π−1(H), where H ⊂ ℂPn denotes a hyperplane divisor.
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BibTeX
@misc{kamenova2026lagrangian,
title = {{Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one}},
author = {Ljudmila Kamenova and Misha Verbitsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14804},
eprint = {2609.14804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14804},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one
AU - Ljudmila Kamenova
AU - Misha Verbitsky
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14804
UR - https://arxiv.org/abs/2609.14804
AB - Let f: M → ℂP^n be a Lagrangian fibration on a compact hyperkahler manifold. We prove that f has no multiple fibers in codimension 1. We prove that this condition is equivalent to the primitivity of the fundamental class of π^−1(H), where H ⊂ ℂP^n denotes a hyperplane divisor.
ER -