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Abstract
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Let
be an isolated
hypersurface singularity with
.
Let
be the ideal
generated by all
-th order
partial derivative of
.
For
, the
new object
is defined to be the Lie algebra of derivations of the new
-th local
algebra
, where
. Its dimension is
denoted as
. This number
is a new numerical analytic
invariant. We compute
for fewnomial isolated singularities (binomial, trinomial) and obtain the formulas
of
.
We also formulate a sharp upper estimate conjecture for the
of
weighted homogeneous isolated hypersurface singularities and verify this conjecture for
large class of singularities. Furthermore, we formulate another inequality conjecture:
,
and verify it for low-dimensional fewnomial singularities.
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Keywords
isolated hypersurface singularity, Lie algebra, local
algebra
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Mathematical Subject Classification
Primary: 14B05, 32S05
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Milestones
Received: 15 February 2021
Revised: 30 May 2021
Accepted: 16 July 2021
Published: 10 November 2021
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