A Course on Constructive Desingularization and Equivariance

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Resolution of Singularities (2004, background): “Since then several accessible proofs of canonical equivariant resolution have emerged ([73], [13], [38], [39],[15],[37]).”
Singularities in positive characteristic, stratification and simplification of the singular locus (2008, methodology): “For more details we refer the reader to the introductory presentation in [11].”
A new proof of desingularization over fields of characteristic zero. (2001, methodology): “Let us mention that the algorithm of resolution of basic objects treated in [16], and implemented in MAPLE by Bodnár and Schicho, is available at http: //www.”
A Simplified Proof of Desingularization and Applications (2002, methodology): “Theorem 3.10. [35, Theorem 7.3.] [ 18, Theorem 7.13. ] Given a basic object (W,(J, b), E) where W is smooth over a field of characteristic zero, there is a resolution, i.e.”
Moduli of affine schemes with reductive group action (2003, methodology): “Using equivariant desingularization [ EV00 ], we may assume that X is nonsingular.”