Stability of local rings of dimension 2.

Abstract:

:The notion of stability of a local ring arises naturally in investigating completed moduli spaces via geometric invariant theory. A scheme corresponding to a boundary point of a moduli space of nonsingular varieties cannot have unstable singular points. This paper reports some results concerning the stability of surface singularities. If a two-dimensional Cohen-Macaulay local ring R is semistable, its multiplicity must be less than seven and either equal to or 1 less than its embedding dimension. If the multiplicity of R is equal to its embedding dimension, the singularity of R must be a simple or cyclic elliptic singularity or the nonnormal limit of such a singularity. The results for the case when the multiplicity of R is less than its embedding dimension are still incomplete; the possible singularities that may arise when the multiplicity of R is equal to 2 or 3 are described.

authors

Shah J

doi

10.1073/pnas.75.9.4085

subject

Has Abstract

pub_date

1978-09-01 00:00:00

pages

4085-6

issue

9

eissn

0027-8424

issn

1091-6490

journal_volume

75

pub_type

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