Cyclic Nielsen realization for del Pezzo surfaces
Geometric Topology
2025-04-25 v1 Algebraic Geometry
Abstract
The cyclic Nielsen realization problem for a closed, oriented manifold asks whether any mapping class of finite order can be represented by a homeomorphism of the same order. In this article, we resolve the smooth, metric, and complex cyclic Nielsen realization problem for certain "irreducible" mapping classes on the family of smooth 4-manifolds underlying del Pezzo surfaces. Both positive and negative examples of realizability are provided in various settings. Our techniques are varied, synthesizing results from reflection group theory and 4-manifold topology.
Cite
@article{arxiv.2504.17235,
title = {Cyclic Nielsen realization for del Pezzo surfaces},
author = {Seraphina Eun Bi Lee and Tudur Lewis and Sidhanth Raman},
journal= {arXiv preprint arXiv:2504.17235},
year = {2025}
}
Comments
37 pages, 1 figure