RT info:eu-repo/semantics/article
T1 Nash multiplicity sequences and Hironaka's order function
A1 Bravo, Ana
A1 Encinas Carrión, Santiago
A1 Pascual Escudero, Beatriz
K1 Resolución de singularidades
K1 Resolution of Singularities
AB When X is a d-dimensional variety defined over a field k of characteristic zero, a constructiveresolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.
PB Indiana University Mathematics Journal
SN 0022-2518
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/35935
UL http://uvadoc.uva.es/handle/10324/35935
LA eng
NO Indiana University Mathematics Journal, 2018 (in press)
NO Producción Científica
DS UVaDOC
RD 22-dic-2024