Logarithmic transformations on the six-sphere

We show that there are infinitely many choices of the multiplicities in the logarithmic transformation step of the Alpöge--Claude construction which produce a complex threefold diffeomorphic to the six-sphere. Moreover, distinct choices of the multiplicities yield biholomorphically inequivalent complex structures.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39102
Primary Topic
Geometry and complex manifolds
Type
preprint
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preprint

Logarithmic transformations on the six-sphere

Jeff Viaclovsky
arXiv (Cornell University)
Geometry and complex manifolds
preprint

Logarithmic transformations on the six-sphere

Jeff Viaclovsky
preprint en

Abstract

We show that there are infinitely many choices of the multiplicities in the logarithmic transformation step of the Alpöge--Claude construction which produce a complex threefold diffeomorphic to the six-sphere. Moreover, distinct choices of the multiplicities yield biholomorphically inequivalent complex structures.

arXiv (Cornell University)
Geometry and complex manifolds
DOIOpen Access PDFOpenAlex
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Logarithmic transformations on the six-sphere — Jeff Viaclovsky · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS