Resumen

VILLAMAYOR U., Orlando. Differential operators on smooth schemes and embedded singularities. Rev. Unión Mat. Argent. [online]. 2005, vol.46, n.2, pp.1-18. ISSN 0041-6932.

Differential operators on smooth schemes have played a central role in the study of embedded desingularization. J. Giraud provides an alternative approach to the form of induction used by Hironaka in his Desingularization Theorem (over fields of characteristic zero). In doing so, Giraud introduces technics based on differential operators. This result was important for the development of algorithms of desingularization in the late 80's (i.e. for constructive proofs of Hironaka's theorem). More recently, differential operators appear in the work of J. Wlodarczyk ([35]), and also on the notes of J. Kollár ([25]). The form of induction used in Hironaka's Desingularization Theorem, which is a form of elimination of one variable, is called maximal contact. Unfortunately it can only be formulated over fields of characteristic zero. In this paper we report on an alternative approach to elimination of one variable, which makes use of higher differential operators. These results open the way to new invariants for singularities over fields of positive characteristic ([34]).

Palabras clave : Resolution of singularities; Desingularization.

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