Advanced Studies in Pure Mathematics

Maximal divisorial sets in arc spaces

Shihoko Ishii

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Abstract

In this paper we introduce a maximal divisorial set in the arc space of a variety. The generalized Nash problem is reduced to a translation problem of the inclusion of two maximal divisorial sets. We study this problem and show a counter example to the most natural expectation even for a non-singular variety.

Article information

Source
Algebraic Geometry in East Asia — Hanoi 2005, K. Konno and V. Nguyen-Khac, eds. (Tokyo: Mathematical Society of Japan, 2008), 237-249

Dates
Received: 3 April 2006
Revised: 14 June 2006
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545001308

Digital Object Identifier
doi:10.2969/aspm/05010237

Mathematical Reviews number (MathSciNet)
MR2409559

Zentralblatt MATH identifier
1162.14022

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 14M99: None of the above, but in this section

Keywords
arc space valuation Nash problem

Citation

Ishii, Shihoko. Maximal divisorial sets in arc spaces. Algebraic Geometry in East Asia — Hanoi 2005, 237--249, Mathematical Society of Japan, Tokyo, Japan, 2008. doi:10.2969/aspm/05010237. https://projecteuclid.org/euclid.aspm/1545001308


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