Reconstruction of a Hypersurface Singularity From its Moduli Algebra

Resumo: In the 1980s, Mather and Yau, followed by Gaffney and Hauser, obtained results guaranteeing that certain algebras (or modules) associated with complex analytic singularities concentrate all the information of their analytic/biholomorphic class. In this talk I intend to report on a recent result dealing with the detection of when a given algebra is associated with a hypersurface singularity, isolated or not, and the question of how to effectively find such a hypersurface.

Reference: Olmedo Rodrigues, J. H. Reconstruction of a hypersurface singularity from its moduli algebra. Res Math Sci 11, 12 (2024).