Invisible singularities in complex algebraic geometry

Maurício Corrêa, János Kollár, Stefan Schreieder, Botong Wang

arXiv:2608.10973v1 Primary: math.AG Secondary: math.CV

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.

Disclosure

“v)]) implies that f ∗ ω has no zeros, and so f is smooth. This forces g to be smooth as well. □ AI disclosure The mathematical content of the paper is due to the authors. ChatGPT was used by one of us to assist with parts of the drafting process. Acknowledgements We are grateful to Javier Fernández de Bobadilla, Feng Hao, Claudio Llosa–Isenrich, Simone Noja, Simon Pietig,”
PDF page 24

Classification: Drafting limited passages
Multiplier: 5
Verified: 2026-08-23T05:09:43.959743Z

Structural counts

Pages 27 pdf

Theorems 9 source

Lemmas 7 source

Propositions 6 source

Corollaries 9 source

Definitions 2 source

Displayed equations 94 source

Bibliography entries 46 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file invisible.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.