التفاصيل البيبلوغرافية
| العنوان: |
Local tropicalizations of splice type surface singularities |
| المؤلفون: |
Cueto, Maria Angelica, Popescu-Pampu, Patrick, Stepanov, Dmitry |
| المساهمون: |
Department of Mathematics Ohio State University OSU, Laboratoire Paul Painlevé - UMR 8524 LPP, Moscow Institute of Physics and Technology Moscow MIPT |
| بيانات النشر: |
Springer Verlag |
| سنة النشر: |
2024 |
| المجموعة: |
LillOA (Lille Open Archive - Université de Lille) |
| مصطلحات موضوعية: |
splice type singularities, toric geometry, toroidal varieties, tropical geometry, Complete intersection singularities, integral homology spheres, Kato-Nakayama spaces, local tropicalization, log geometry, Milnor fibers, Newton non-degeneracy, real oriented blowups, rounding, Seifert fibrations, surface singularities |
| الوصف: |
Splice type surface singularities were introduced by Neumann and Wahl as a generalization of the class of Pham–Brieskorn–Hamm complete intersections of dimension two. Their construction depends on a weighted tree called a splice diagram. In this paper, we study these singularities from the tropical viewpoint. We characterize their local tropicalizations as the cones over the appropriately embedded associated splice diagrams. As a corollary, we reprove some of Neumann and Wahl’s earlier results on these singularities by purely tropical methods, and show that splice type surface singularities are Newton non-degenerate complete intersections in the sense of Khovanskii. We also confirm that under suitable coprimality conditions on its weights, the diagram can be uniquely recovered from the local tropicalization. As a corollary of the Newton non-degeneracy property, we obtain an alternative proof of a recent theorem of de Felipe, González Pérez and Mourtada, stating that embedded resolutions of any plane curve singularity can be achieved by a single toric morphism, after re-embedding the ambient smooth surface germ in a higher-dimensional smooth space. The paper ends with an appendix by Jonathan Wahl, proving a criterion of regularity of a sequence in a ring of convergent power series, given the regularity of an associated sequence of initial forms. |
| نوع الوثيقة: |
article in journal/newspaper |
| وصف الملف: |
application/octet-stream |
| اللغة: |
English |
| Relation: |
Centre Européen pour les Mathématiques, la Physique et leurs Interactions; Géométrie Lipschitz des singularités; Mathematische Annalen; http://hdl.handle.net/20.500.12210/121859 |
| الاتاحة: |
https://hdl.handle.net/20.500.12210/121859 |
| Rights: |
info:eu-repo/semantics/openAccess |
| رقم الانضمام: |
edsbas.6C90033B |
| قاعدة البيانات: |
BASE |