Coordinates at stable points of the space of arcs

JOURNAL OF ALGEBRA

卷:494

Article

Reguera, Ana J.¹ 

[1] Univ Valladolid, Dept Algebra Anal Matemat Geometria & Topol, Paseo Belen 7, E-47011 Valladolid, Spain

关键词: Space of arcs;    Divisorial valuation;    Graded algebra;   

DOI  :  10.1016/j.jalgebra.2017.09.031

来源: Elsevier

【 摘 要 】

Let X be a variety over a field k and let X-infinity, be its space of arcs. Let P-E be the stable point of X-infinity defined by a divisorial valuation v(E) on X. Assuming char k = 0, if X is smooth at the center of P-E, we make a study of the graded algebra associated to v(E) and define a finite set whose elements generate a localization of the graded algebra moduloetale covering. This provides an explicit description of a minimal system of generators of the local ring O-X infinity,O-PE. If X is singular, we obtain generators of P-E / P-E(2) and conclude that embdim O-(X,O-infinity)red,O-pE = embdim (O-x infinity,O-pE) over cap (k) over cap (E) + 1 where (k) over cap (E) is the Mather discrepancy of X with respect to v(E). This provides algebraic tools for explicit computations of the local rings (O-X infinity,O-pE) over cap . (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free