On Lipschitz Normally Embedded complex surface germs
Algebraic Geometry
2022-06-01 v4
Abstract
We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prove in particular that the topological type of such a germ determines the combinatorics of its minimal resolution which factors through the blowup of its maximal ideal and through its Nash transform, as well as the polar curve and the discriminant curve of a generic plane projection, thus generalizing results of Spivakovsky and Bondil that were known for minimal surface singularities. In an appendix, we give a new example of a Lipschitz Normally Embedded surface singularity.
Cite
@article{arxiv.2006.01773,
title = {On Lipschitz Normally Embedded complex surface germs},
author = {André Belotto da Silva and Lorenzo Fantini and Anne Pichon},
journal= {arXiv preprint arXiv:2006.01773},
year = {2022}
}
Comments
v4: New appendix with the proof of a folklore result. A few corrections made, exposition improved. 34 pages, 2 figures. To appear in Compositio Mathematica