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D.5.5.2 blowUp2
Procedure from library resolve.lib (see resolve_lib).
- Usage:
- blowUp2(J,C);
J,C = ideals,
- Assume:
- C = ideal containing J
- Note:
- C the ideal of the center of the blowup and J the ideal
of the variety
Important differences to blowUp:
- V(J) itself is blown up, not the ambient space
- C is not assumed to be non-singular
- Compute:
- the blowing up of J in C, the exceptional locus and the blow-up
map
- Return:
- list, say l, of size at most size(C),
l[i] is the affine ring corresponding to the i-th chart
each l[i] contains the ideals
- Jnew, ideal of the blownup J
- eD, ideal of the new exceptional divisor
- bM, ideal corresponding to the blowup map
Example:
| | LIB "resolve.lib";
ring r=0,(x,y,z),dp;
ideal I=z2-x^3*y^2;
ideal C=z,xy;
list li=blowUp2(I,C);
size(li); // number of charts
==> 2
def S1=li[1];
setring S1; // chart 1
basering;
==> // characteristic : 0
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x(1) x(3) y(2)
==> // block 2 : ordering C
Jnew;
==> Jnew[1]=x(1)*y(2)^2-1
eD;
==> eD[1]=x(3)
==> eD[2]=x(1)*y(2)^2-1
bM;
==> bM[1]=x(1)
==> bM[2]=x(3)*y(2)^3
==> bM[3]=x(3)
def S2=li[2];
setring S2; // chart 2
basering;
==> // characteristic : 0
==> // number of vars : 2
==> // block 1 : ordering dp
==> // : names x(2) y(1)
==> // block 2 : ordering C
Jnew;
==> Jnew[1]=0
eD;
==> eD[1]=x(2)*y(1)^2
bM;
==> bM[1]=y(1)^2
==> bM[2]=x(2)
==> bM[3]=x(2)*y(1)^3
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