Hodge theory and topology of Bogomolov--Guan manifolds
Abstract
Bogomolov--Guan manifolds are simply connected, irreducible holomorphic symplectic manifolds that are not Kähler, yet they echo hyperkähler geometry in striking ways. We show that their Frölicher spectral sequence degenerates at E1 and that their Hodge numbers are stable under small deformations. The general fibers of their natural Lagrangian fibration are rationally null-homologous, and the Beauville--Bogomolov--Fujiki form is degenerate. Despite this, in every dimension, the Euler characteristics agree with those of generalized Kummer manifolds. In dimensions four and six, we compute the full Hodge diamonds and all Chern and Pontryagin numbers. Surprisingly, these characteristic numbers are the same as the generalized Kummer ones, even though the Betti numbers differ and the Hodge diamonds are asymmetric.
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BibTeX
@misc{kurnosov2026hodge,
title = {{Hodge theory and topology of Bogomolov--Guan manifolds}},
author = {Nikon Kurnosov and Ángel David Ríos Ortiz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01210},
eprint = {2611.01210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01210},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hodge theory and topology of Bogomolov--Guan manifolds
AU - Nikon Kurnosov
AU - Ángel David Ríos Ortiz
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01210
UR - https://arxiv.org/abs/2611.01210
AB - Bogomolov--Guan manifolds are simply connected, irreducible holomorphic symplectic manifolds that are not Kähler, yet they echo hyperkähler geometry in striking ways. We show that their Frölicher spectral sequence degenerates at E_1 and that their Hodge numbers are stable under small deformations. The general fibers of their natural Lagrangian fibration are rationally null-homologous, and the Beauville--Bogomolov--Fujiki form is degenerate. Despite this, in every dimension, the Euler characteristics agree with those of generalized Kummer manifolds. In dimensions four and six, we compute the full Hodge diamonds and all Chern and Pontryagin numbers. Surprisingly, these characteristic numbers are the same as the generalized Kummer ones, even though the Betti numbers differ and the Hodge diamonds are asymmetric.
ER -