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oai:docta.ucm.es:20.500.14352/72052023-08-11T07:47:18Zcom_20.500.14352_14col_20.500.14352_15

The Tjurina number for Sebastiani-Thom type isolated hypersurface singularities Almirón, Patricio 517.554 Singularities of curves Singularities of surfaces Local complex singularities Hypersurface singularities Funciones (Matemáticas) Geometria algebraica 1202 Análisis y Análisis Funcional 1201.01 Geometría Algebraica In this note we provide a formula for the Tjurina number of a join of isolated hypersurface singularities in separated variables. From this we are able to provide a characterization of isolated hypersurface singularities whose difference between the Milnor and Tjurina numbers is less or equal than two arising as the join of isolated hypersurface singularities in separated variables. Also, we are able to provide new upper bounds for the quotient of Milnor and Tjurina numbers of certain join of isolated hypersurface singularities. Finally, we deduce an upper bound for the quotient of Milnor and Tjurina numbers in terms of the singularity index of any isolated hypersurface singularity, not necessarily a join of singularities. Ministerio de Ciencia e Innovación (MICINN) Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) FALSE unpub 2023-06-17T08:28:00Z 2023-06-17T08:28:00Z 2021 journal article https://hdl.handle.net/20.500.14352/7205 XXXX-XXXX eng MTM2016-76868-C2-1-P; PID2020-114750GB-C32 open access application/pdf