PreprintCC BY 4.0arXiv
The topology of Kähler manifolds and 1-forms without zeros
Abstract
We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In particular, we construct a smooth projective variety for which the Aomoto complex is exact for every nonzero holomorphic one-form and every semisimple local system, although every closed real one-form, and hence every holomorphic one-form, has a zero.
Related
- Holomorphic 1-forms without zeros on Kähler manifolds
- Extremal Kähler--Ricci solitons on Fano manifolds are Kähler--Einstein
- Finite-Time Singularities of the Kähler--Ricci Flow on a ℂPm-Bundle over a Product of Kähler--Einstein Manifolds
- Zeros of Quasimodular Forms Defined by Iterated Sums
- On products of locally conformally Kähler manifolds
BibTeX
@misc{correa2026topology,
title = {{The topology of Kähler manifolds and 1-forms without zeros}},
author = {Maurício Corrêa and János Kollár and Stefan Schreieder and Botong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04314},
eprint = {2610.04314},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04314},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The topology of Kähler manifolds and 1-forms without zeros
AU - Maurício Corrêa
AU - János Kollár
AU - Stefan Schreieder
AU - Botong Wang
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04314
UR - https://arxiv.org/abs/2610.04314
AB - We study how the topology and geometry of a compact Kähler manifold relate to the zeros of its one-forms. We determine all implications among several closely related conditions. In particular, we construct a smooth projective variety for which the Aomoto complex is exact for every nonzero holomorphic one-form and every semisimple local system, although every closed real one-form, and hence every holomorphic one-form, has a zero.
ER -