|
V-Filtration - An Example
LIB "gaussman.lib";
ring r=0,(x,y),ds;
poly f=x5+x2y2+y5;
The command vfiltration(f) returns a list
V :
-
V[1] contains the spectral numbers
a[i] in increasing order.
-
V[2] contains the corresponding
multiplicities.
-
V[3] contains a list of vector space bases for
GrVa[i](H''/H') in
terms of V[4].
-
V[4] contains a monomial vector space basis for
(H''/H').
list V=vfiltration(f);
print(V[1]);
|
==>
|
-1/2, -3/10, -1/10, 0, 1/10, 3/10, 1/2
|
print(V[2])
Vector space bases of the corresponding graded parts of the
V-filtration:
for (int i=1; i<=7; i++) { print(matrix(V[4])*V[3][i]); }
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
0 |
0 |
0 |
0 |
0 |
0 |
6 |
0 |
0 |
0 |
0 |
0 |
0 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
4 |
0 |
0 |
0 |
0 |
0 |
1 |
2 |
3 |
5 |
6 |
0 |
0 |
|
Interprete:
xayb =
[xayb dx ^ dy]
in
H''/H'.
Spectrum and V-filtration
|