Innovating Works

GTSP

Financiado
Geometry and Topology of Singularities
This interdisciplinary project brings together innovative ideas and techniques from algebraic geometry and complex analytic geometry, singularity theory, commutative algebra and topology. Given two complex analytic varieties X and... This interdisciplinary project brings together innovative ideas and techniques from algebraic geometry and complex analytic geometry, singularity theory, commutative algebra and topology. Given two complex analytic varieties X and X' that are part of an analytic family in a complex affine space we will study the relationships between the different similarities X and X' might share. Such similarities can be of geometric and topological nature.The synonym for similarity we will use here is equisingularity. We say X and X' are topologically equisingular if there is a homeomorphism between X and X' that extends to an ambient homomorphism that trivializes the entire family; we say that X and X' are geometrically equisingular if X and X' have similar resolution of singularities, or if a resolution of the entire family induces a resolution of each fiber. Understanding the topology of either X or X' usually involves a continuous deformation of either one of them to a smooth variety, the existence of which is guaranteed under a special smoothability hypothesis.  A stronger version of topological equisingularity, called Lipschitz equisingularity, asks for a homeomorphism between X and X' that satisfies the Lipschitz inequality. The ultimate goal of the project is to gain insight in the relationships between topological (Lipschitz) and geometric equisingularity  and develop an approach to study the topology of singularities that are not necessarily smoothable without imposing special dimension (or codimension) assumptions as was done previously. ver más
31/08/2025
CNRS
196K€
Perfil tecnológico estimado
Duración del proyecto: 27 meses Fecha Inicio: 2023-05-16
Fecha Fin: 2025-08-31

Línea de financiación: concedida

El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-05-16
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2022-PF-01-01: MSCA Postdoctoral Fellowships 2022
Cerrada hace 2 años
Presupuesto El presupuesto total del proyecto asciende a 196K€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5