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Methods of commutative algebra and algebraic geometry in singularity theory.


This project hinges on the impact of the fine theory of ideals in singularities. The informal designation ``fine theory'' refers to arithmetical and homological properties of ideals which lead to a deep intertwining with purely geometric properties of algebraic varieties and their classification. This cooperation naturally disembarks in singularity theory.Venturing facilitating the reader's insertion in the contents proper of the project, we divide it along the following general themes:1.Blowup methods2.Differential methods3.Birational methods (AU)