33,217 research outputs found
Deforming nonnormal isolated surface singularities and constructing 3-folds with as exceptional set
Normally one assumes isolated surface singularities to be normal. The purpose
of this paper is to show that it can be useful to look at nonnormal
singularities. By deforming them interesting normal singularities can be
constructed, such as isolated, non Cohen-Macaulay threefold singularities. They
arise by a small contraction of a smooth rational curve, whose normal bundle
has a sufficiently positive subbundle. We study such singularities from their
nonnormal general hyperplane section.Comment: 20
Conformal Bootstrap Analysis for Single and Branched Polymers
The determinant method in the conformal bootstrap is applied for the critical
phenomena of a single polymer in arbitrary dimensions. The scale dimensions
(critical exponents) of the polymer () and the branched polymer () are obtained from the small determinants. It is known that the
dimensional reduction of the branched polymer in dimensions to Yang-Lee
edge singularity in - dimensions holds exactly. We examine this
equivalence by the small determinant method.Comment: 13 pages, 5 figure
On the last Hilbert-Samuel coefficient of isolated singularities
In 1978 Lipman presented a proof of the existence of a desingularization for
any excellent surface. The strategy of Lipman's proof is based on the
finiteness of the number H(R) defined as the supreme of the second
Hilbert-Samuel coefficient I, where I range the set of normal m-primary ideals
of a Noetherian complete local ring (R,m). The problem studied in the paper is
the extension of the result of Lipman on H(R) to m-primary ideals I of a
d-dimensional Cohen-Macaulay ring R such that the associated graded ring of R
with respect to I^n is Cohen-Macaulay for n>> 0
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