Work

Invisible singularities in complex algebraic geometry

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.10973

Authors: Corrêa, Maurício, Kollár, János, Schreieder, Stefan, Wang, Botong

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Science Foundation Ireland, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni

Award: G5089335471

OpenAlex ID: W7202291783

Cites: 5

Cited by: 2

Related to: 10