Strong resolution of singularities in characteristic zero

By Santiago Encinas, Herwig Hauser. 2002

152 citations recorded by the source corpus.

Abstract. We present a concise proof for the existence and construction of a strong resolution of excellent schemes of finite type over a field of characteristic zero. Our proof is based on earlier work of Villamayor, Encinas-Villamayor and Bierstone-Milman. It proposes some substantial simplifications which may be helpful for a better understanding of how to prove Hironaka's famous theorem on embedded resolution of singularities.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ca7ef4b567e9717b9195fe719a4a6e48237dc439

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Resolution of singularities for 3-folds in positive characteristic (2006, background): “appeared, making the proof quite accessible now, including Abramovich and de Jong [AJo], Bierstone and Milman [BrM], Bogomolov and Pantev [BP], Bravo, Encinas and Villamayor [BEV], Encinas and Hauser [EH], Encinas and Villamayor [EV], Hauser [Hau2], Koll´ar [Ko], Villamayor [V], Wlodarczyk [W]. Most”
A Simplified Proof of Desingularization and Applications (2002, methodology): “Finally, there are other results in desingularization within this new framework and related to this one: For instance, Matsuki’s lucid presentation of the ideas behind the algorithms of desingularization in [28], which is based in the work developed in [19]; or [15], where an algorithm of principali”
Simple Hironaka resolution in characteristic zero (2004, methodology): “What adds to complexity is that the invariant is defined within some rich inductive scheme encoding the desingularization and assuring its canonicity ( Bierstone-Milman’s towers of local blow-ups with admissible centers and Villamayor’s generalized basic objects) (see also Encinas-Hauser [15]).”
On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for) (2009, background): “order of I− is constant along Z, a property that is achieved through the insertion of companion ideals as suggested by Villamayor, cf. [EV2, EH ]).”
Resolution of Singularities (2004, background): “Some of the recent papers on this area are: Hauser [50], Heinzer, Rotthaus and Wiegand [51], Kuhlmann [59], [60], Piltant [71], Spivakovsky [77], Teissier [78].”