Symplectic Monodromy at radius 0 and equimultiplicity of families of hypersurfaces with constant Milnor number
Javier Fernandez de Bobadilla
Basque Center for Applied Mathematics
http://www.bcamath.org/en/people/jbobadilla
Date(s) : 16/06/2022 iCal
14h00 - 15h00
Abstract: (joint work with T. Pelka) We prove the Zariski multiplicity conjecture for families of isolated hypersurface singularities. For it we show how to construct a symplectic monodromy « at radius 0 » with very special dynamical properties, which is symplectically isotopic by radius variation to the usual symplectic monodromy at positive small radius . For this we use a hybrid construction employing log-geometry (Kato-Nakayama spaces) and tropical geometry. In particular our construction provides an smooth atlas in the topological space used by A’Campo for his study of monodromy zeta function and Lefschetz numbers, and provides an alternate construction of special symplectic monodromy representatives due to McLean which is better suited for the study of families and degenerations. Then we use a slight generalization of a spectral sequence in Floer Homology (due to McLean) to recover multiplicity, and properties of invariance of Floer homology along symplectic isotopies to prove its constancy in Milnor number constant families.
Zoom connection details / coordonnées de la réunion Zoom :
Sujet : Séminaire de Géométrie de Marseille
Heure : 16 juin 2022 01:45 PM Paris
https://univ-amu-fr.zoom.us/j/83088710342?pwd=ZUpwWTVvNW1vN0FJQ0dSQ3BpQ0FLZz09
ID de réunion : 830 8871 0342
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