RT Journal Article
T1 Nash multiplicity sequences and Hironaka's order function
A1 Bravo, Ana
A1 Pascual Escudero, Beatriz
A1 Encinas, S.
AB When X is a d-dimensional variety deﬁned over a ﬁeld k of characteristic zero, a constructive resolution 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 2020
FD 2020
LK https://hdl.handle.net/10016/33982
UL https://hdl.handle.net/10016/33982
LA eng
NO The authors were partially supported by MTM2015-68524-P. The third author was supported by BES-2013-062656.
DS e-Archivo
RD 14 jul. 2024