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D.15.9.3 embR
Procedure from library resjung.lib (see resjung_lib).
- Usage:
- embR(ideal C);
C = ideal
- Assume:
- C = ideal of plane curve
- Return:
- a list l of rings
l[i] is a ring containing a basic object BO, the result of the
resolution.
- Theory:
- Given a plain curve C, an embedded resolution of this curve
by means of a sequence of blow ups at singular points of C is
computed such that the resulting total transform consists
of non-singular components and only has strict normal crossings.
The result of each blow up is represented by means of
affine charts and hence also the final result is represented in
charts, which are collected in a list l of rings. Each ring
in this list corresponds to one chart. The collection of
data describing the ambient space, the strict transform, the
exceptional divisors and the combination of the blow ups
leading to this chart is contained in the list BO which resides
in this ring.
- Note:
- - The best way to look at the data contained in BO is the
procedure showBO from the library resolve.lib.
- The algorithm does not touch normal crossings of V(C).
Example:
| LIB "resjung.lib";
ring R=0,(x,y),dp;
ideal C=x2-y3;
list li=embR(C);
==> // ** killing the basering for level 0
==> // ** killing the basering for level 1
def S=li[1];
setring S;
showBO(BO);
==>
==> ==== Ambient Space:
==> _[1]=0
==>
==> ==== Ideal of Variety:
==> _[1]=y(1)-1
==>
==> ==== Exceptional Divisors:
==> [1]:
==> _[1]=1
==> [2]:
==> _[1]=y(1)
==> [3]:
==> _[1]=x(2)
==>
==> ==== Images of variables of original ring:
==> _[1]=x(2)^3*y(1)^2
==> _[2]=x(2)^2*y(1)
==>
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