PreprintCC BY 4.0arXiv
Multicomplexes in Action: Strong Formality of Compact Hyperkähler Manifolds
Abstract
We show that all compact hyperkähler manifolds are bigraded strongly formal in the sense of Milivojević and Stelzig, proving that in the context of pluripotential homotopy theory they play the same role as compact Kähler manifolds in rational homotopy theory. Indeed, the main result arises from general algebraic considerations on categories of objects with more differentials, that of multicomplexes and commutative n-differential graded algebras. For them we discuss a standard model category structure, introduce a generalization of the ∂∂̅-Lemma and establish an algebraic formality theorem.
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BibTeX
@misc{contro2026multicomplexes,
title = {{Multicomplexes in Action: Strong Formality of Compact Hyperkähler Manifolds}},
author = {Antonio Pio Contrò},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40639},
eprint = {2610.40639},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40639},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multicomplexes in Action: Strong Formality of Compact Hyperkähler Manifolds
AU - Antonio Pio Contrò
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40639
UR - https://arxiv.org/abs/2610.40639
AB - We show that all compact hyperkähler manifolds are bigraded strongly formal in the sense of Milivojević and Stelzig, proving that in the context of pluripotential homotopy theory they play the same role as compact Kähler manifolds in rational homotopy theory. Indeed, the main result arises from general algebraic considerations on categories of objects with more differentials, that of multicomplexes and commutative n-differential graded algebras. For them we discuss a standard model category structure, introduce a generalization of the ∂∂̅-Lemma and establish an algebraic formality theorem.
ER -