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(Q3730)
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English
math0011097.11
No description defined
Statements
defining formula
es
(
C
)
=
τ
(
C
)
+
∑
i
=
1
s
(
b
i
+
1
)
+
∑
i
∈
T
(
l
(
i
)
−
m
(
i
)
)
−
∑
P
∈
IN
(
C
)
1
2
(
m
P
2
+
m
p
−
4
)
{\displaystyle \operatorname {es} (C)=\tau (C)+\sum _{i=1}^{s}(b_{i}+1)+\sum _{i\in T}\left(l(i)-m(i)\right)-\sum _{P\in \operatorname {IN} (C)}{\tfrac {1}{2}}(m_{P}^{2}+m_{p}-4)}
0 references
in defining formula
C
{\displaystyle C}
symbol represents
curve
0 references
i
{\displaystyle i}
symbol represents (string)
Index variable
0 references
p
{\displaystyle p}
symbol represents
multiplicity
0 references
N
{\displaystyle N}
symbol represents (string)
Number of exceptional curves
0 references
m
{\displaystyle m}
symbol represents
multiplicity
0 references
P
∈
IN
(
C
)
{\displaystyle P\in \operatorname {IN} (C)}
symbol represents
Infinitely near point
0 references
m
(
i
)
{\displaystyle m(i)}
symbol represents
multiplicity
0 references
τ
(
C
)
{\displaystyle \tau (C)}
symbol represents (string)
Tjurina number
0 references
l
(
i
)
{\displaystyle l(i)}
symbol represents (string)
conductor number
0 references
m
p
{\displaystyle m_{p}}
symbol represents (string)
multiplicity of an infinitely near point
0 references
i
∈
T
{\displaystyle i\in T}
symbol represents (string)
Index of a branch in a curve singularity
0 references
m
P
{\displaystyle m_{P}}
symbol represents
multiplicity
0 references
IN
(
C
)
{\displaystyle \operatorname {IN} (C)}
symbol represents (string)
infinitely near points
0 references
l
{\displaystyle l}
symbol represents (string)
conductor number on branch C_i
0 references
s
{\displaystyle s}
symbol represents (string)
exceptional curves
0 references
b
i
{\displaystyle b_{i}}
symbol represents (string)
Self-Intersection Numbers
0 references
T
{\displaystyle T}
symbol represents (string)
Smooth Curve Germ
0 references
es
(
C
)
{\displaystyle \operatorname {es} (C)}
symbol represents (string)
Equisingularity Index of C
0 references
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⧼wikibase-sitelinks-mathematics⧽
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