INNER GEOMETRY OF COMPLEX SURFACES: A VALUATIVE APPROACH
| Autor: | André Belotto da Silva, Lorenzo Fantini, Anne Pichon |
|---|---|
| Přispěvatelé: | Aix Marseille Université (AMU), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0023,LISA,Géométrie Lipschitz des singularités(2017), Pichon, Anne, Géométrie Lipschitz des singularités - - LISA2017 - ANR-17-CE40-0023 - AAPG2017 - VALID, Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Geometry and Topology Geometry and Topology, In press |
| ISSN: | 1465-3060 1364-0380 |
| Popis: | Given a complex analytic germ $(X, 0)$ in $(\mathbb C^n, 0)$, the standard Hermitian metric of $\mathbb C^n$ induces a natural arc-length metric on $(X, 0)$, called the inner metric. We study the inner metric structure of the germ of an isolated complex surface singularity $(X,0)$ by means of an infinite family of numerical analytic invariants, called inner rates. Our main result is a formula for the Laplacian of the inner rate function on a space of valuations, the non-archimedean link of $(X,0)$. We deduce in particular that the global data consisting of the topology of $(X,0)$, together with the configuration of a generic hyperplane section and of the polar curve of a generic plane projection of $(X,0)$, completely determine all the inner rates on $(X,0)$, and hence the local metric structure of the germ. Several other applications of our formula are discussed in the paper. Comment: Proposition 5.3 strengthened, exposition improved, some typos corrected, references updated. 42 pages and 10 figures. To appear in Geometry & Topology |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|