Resolution of Foliated Varieties by Torus Actions - A Desingularization Approach

Explore a 53-minute conference talk delivered at the Centre International de Rencontres Mathématiques during the thematic meeting "Logarithmic and non-archimedean methods in Singularity Theory" that delves into the resolution of singular foliations on analytic manifolds and algebraic varieties. Learn about the construction of principalization of ideals on smooth foliated varieties in characteristic zero, and discover the proof of desingularization of Darboux totally integrable foliations in arbitrary dimensions. Understand how weighted cobordant blow-ups and torus actions are used to transform generically transverse sections into fully transverse ones. The presentation, which represents joint work with Abramovich, Belotto, and Temkin, demonstrates the connection between this approach and traditional methods of resolving singularities of varieties. Access this mathematical content through CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched metadata, and comprehensive search functionality for an enhanced learning experience.