On (-<Emphasis Type="Italic">P</Emphasis> ? <Emphasis Type="Italic">P</Emphasis>)-constant deformations of Gorenstein surface singularities |
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Authors: | Email author" target="_blank">Tomohiro?OkumaEmail author |
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Institution: | (1) Department of Mathematics, Gunma National College of Technology, 580 Toriba, 371 Gunma Maebashi, Japan |
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Abstract: | Let : X
T be a small deformation of a normal
Gorenstein surface singularity
X
0 =
-1(0) over the complex number field .
Suppose that T is a neighborhood
of the origin of and that
X
0
is not log-canonical.
We show that if a topological invariant
-P
t
P
t
of X
t
= -1(t)
is constant, then, after a suitable finite base change,
admits a simultaneous resolution
f : M
X which induces a locally trivial
deformation of each maximal string of rational curves at an end of
the exceptional set of M
0
X
0;
in particular, if X
0
has a star-shaped resolution graph, then
admits a weak simultaneous resolution (in other words, is
an equisingular deformation). |
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Keywords: | Primary 14B07 Secondary 14E15 32S45 |
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