PreprintCC BY 4.0arXiv
The dual complex and RC-invariant functors
Abstract
We extend the dual complex of a simple normal crossings divisor to a homotopy type invariant 𝒟(X) of arbitrary complex varieties, and we prove that it is contractible when X is connected and of klt type. In fact, the dual complex belongs to a broader class of invariants, which we call RC (rationally connected)-invariant functors. We prove a rigidity theorem governing the behavior of such functors with respect to rationally connected fibrations.
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BibTeX
@misc{burke2026dual,
title = {{The dual complex and RC-invariant functors}},
author = {Andrew Burke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30608},
eprint = {2610.30608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30608},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The dual complex and RC-invariant functors
AU - Andrew Burke
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30608
UR - https://arxiv.org/abs/2610.30608
AB - We extend the dual complex of a simple normal crossings divisor to a homotopy type invariant 𝒟(X) of arbitrary complex varieties, and we prove that it is contractible when X is connected and of klt type. In fact, the dual complex belongs to a broader class of invariants, which we call RC (rationally connected)-invariant functors. We prove a rigidity theorem governing the behavior of such functors with respect to rationally connected fibrations.
ER -