Higher-Page Jacobian and Albanese Tori
Abstract
We construct, through Hodge-theoretical methods, what we call the Er-Jacobian torus, the Er-Albanese torus and the Er-Albanese map of any compact complex manifold that is either {\it page-(r-1)-∂∂̅} or {\it Er-sGG}. These two classes of manifolds, the former of which is contained in the latter, have been introduced recently by both authors jointly with J. Stelzig, respectively by the first-named author. A Hodge theory is also developed for the latter class of manifolds. We then apply our results to give structure theorems and an identity of algebraic dimensions in terms of the Er-Albanese map and torus. Other applications result in cohomological and metrical theorems for the $6$-dimensional sphere when it is equipped either with a hypothetical complex structure or with the complex structures very recently claimed to exist in the literature. For example, we show that in the latter case no {\it strongly Gauduchon} metric exists on S6.
Related
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BibTeX
@misc{popovici2026higherpage,
title = {{Higher-Page Jacobian and Albanese Tori}},
author = {Dan Popovici and Luis Ugarte},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02109},
eprint = {2610.02109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02109},
}
RIS
TY - UNPB
TI - Higher-Page Jacobian and Albanese Tori
AU - Dan Popovici
AU - Luis Ugarte
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02109
UR - https://arxiv.org/abs/2610.02109
AB - We construct, through Hodge-theoretical methods, what we call the E_r-Jacobian torus, the E_r-Albanese torus and the E_r-Albanese map of any compact complex manifold that is either {\it page-(r-1)-∂∂̅} or {\it E_r-sGG}. These two classes of manifolds, the former of which is contained in the latter, have been introduced recently by both authors jointly with J. Stelzig, respectively by the first-named author. A Hodge theory is also developed for the latter class of manifolds. We then apply our results to give structure theorems and an identity of algebraic dimensions in terms of the E_r-Albanese map and torus. Other applications result in cohomological and metrical theorems for the $6$-dimensional sphere when it is equipped either with a hypothetical complex structure or with the complex structures very recently claimed to exist in the literature. For example, we show that in the latter case no {\it strongly Gauduchon} metric exists on S^6.
ER -