PreprintCC BY 4.0arXiv
Invisible singularities in complex algebraic geometry
Abstract
We construct morphisms between smooth complex projective varieties that have singular fibers, but look topologically smooth. We use this to give negative answers to the following four conjectures and questions: the smoothness conjecture of Fernández~de~Bobadilla and Kollár, a question of Kollár and Pardon on universal covers, Kotschick's conjecture on 1-forms, and a conjecture of Schreieder on Aomoto complexes. Version 2 is a revised version of sections 1--6 of the original, no change in the results. A substantially expanded version of sections 7--8 of the original will be posted separately.
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BibTeX
@misc{correa2026invisible,
title = {{Invisible singularities in complex algebraic geometry}},
author = {Maurício Corrêa and János Kollár and Stefan Schreieder and Botong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.10973},
eprint = {2608.10973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10973},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Invisible singularities in complex algebraic geometry
AU - Maurício Corrêa
AU - János Kollár
AU - Stefan Schreieder
AU - Botong Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.10973
UR - https://arxiv.org/abs/2608.10973
AB - We construct morphisms between smooth complex projective varieties that have singular fibers, but look topologically smooth. We use this to give negative answers to the following four conjectures and questions: the smoothness conjecture of Fernández~de~Bobadilla and Kollár, a question of Kollár and Pardon on universal covers, Kotschick's conjecture on 1-forms, and a conjecture of Schreieder on Aomoto complexes. Version 2 is a revised version of sections 1--6 of the original, no change in the results. A substantially expanded version of sections 7--8 of the original will be posted separately.
ER -