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A two-parameter family of complex structures on S6
Abstract
We construct a two-parameter family of complex structures on the standard six-sphere, starting from a rational elliptic surface with singular fibers III*,I1,I1,I1. The resulting torus fibration over ℙ1 has one multiple fiber of multiplicity four, one hexagonal fiber, and two rank-one degenerations. These complex structures are not biholomorphic to the original Alpöge--Claude examples.
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BibTeX
@misc{viaclovsky2026twoparameter,
title = {{A two-parameter family of complex structures on $S^6$}},
author = {Jeff Viaclovsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33785},
eprint = {2609.33785},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33785},
}
RIS
TY - UNPB
TI - A two-parameter family of complex structures on S^6
AU - Jeff Viaclovsky
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33785
UR - https://arxiv.org/abs/2609.33785
AB - We construct a two-parameter family of complex structures on the standard six-sphere, starting from a rational elliptic surface with singular fibers III^*,I_1,I_1,I_1. The resulting torus fibration over ℙ^1 has one multiple fiber of multiplicity four, one hexagonal fiber, and two rank-one degenerations. These complex structures are not biholomorphic to the original Alpöge--Claude examples.
ER -