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D.5.5.8 blowUpBO
Procedure from library resolve.lib (see resolve_lib).
- Usage:
- blowUpBO (BO,C,e);
BO = basic object, a list: ideal W,
ideal J,
intvec b,
list Ex,
ideal ab,
intvec v,
intvec w,
matrix M
C = ideal
e = integer (0 usual blowing up, 1 deleting extra charts, 2 deleting
no charts )
- Assume:
- R = basering, a polynomial ring, W an ideal of R,
J = ideal containing W,
C = ideal containing J
- Compute:
- the blowing up of BO[1] in C, the exeptional locus, the strict
transform of BO[2]
- Note:
- blowUpBO may be applied to basic objects in the sense of
[Bravo, Encinas, Villamayor] in the following referred to as BO and
to presentations in the sense of [Bierstone, Milman] in the following
referred to as BM.
- Return:
- a list l of length at most size(C),
l[i] is a ring containing an object BO resp. BM:
BO[1]=BM[1] an ideal, say Wi, defining the ambient space of the
i-th chart of the blowing up
BO[2]=BM[2] an ideal defining the strict transform
BO[3] intvec, the first integer b such that in the original object
(Delta^b(BO[2]))==1
the subsequent integers have the same property for Coeff-Objects
of BO[2] used when determining the center
BM[3] intvec, BM[3][i] is the assigned multiplicity of BM[2][i]
BO[4]=BM[4] the list of exceptional divisors
BO[5]=BM[5] an ideal defining the map K[W] ----> K[Wi]
BO[6]=BM[6] an intvec BO[6][j]=1 indicates that <BO[4][j],BO[2]>=1,
i.e. the strict transform does not meet the j-th exceptional
divisor
BO[7] intvec,
the index of the first blown-up object in the resolution process
leading to this object for which the value of b was BO[3]
the subsequent ones are the indices for the Coeff-Objects
of BO[2] used when determining the center
BM[7] intvec, BM[7][i] is the index at which the (2i-1)st entry
of the invariant first reached its current maximal value
BO[8]=BM[8] a matrix indicating that BO[4][i] meets BO[4][j] by
BO[8][i,j]=1 for i < j
BO[9] empty
BM[9] the invariant
Example:
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