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A.4.9 Resolution of singularities
Resolution of singularities and applications thereof are provided by the
libraries resolve.lib and reszeta.lib; graphical output may be
generated automatically by using external programs surf and dot
respectively to which a specialized interface is provided by the library
resgraph.lib. In this example, the basic functionality of the
resolution of singularities package is illustrated by the computation of
the intersection matrix and genera of the exceptional curves on a surface
obtained from resolving the A6 surface singularity. A separate tutorial,
which introduces the complete functionality of the package and explains
the rather complicated data structures appearing in intermediate results,
can be found at http://www.singular.uni-kl.de/tutor_resol.ps.
| | LIB"resolve.lib"; // load the resolution algorithm
LIB"reszeta.lib"; // load its application algorithms
ring R=0,(x,y,z),dp; // define the ring Q[x,y,z]
ideal I=x7+y2-z2; // an A6 surface singularity
list L=resolve(I); // compute the resolution
list iD=intersectionDiv(L); // compute intersection properties
iD; // show the output
==> [1]:
==> -2,0,1,0,0,0,
==> 0,-2,0,1,0,0,
==> 1,0,-2,0,1,0,
==> 0,1,0,-2,0,1,
==> 0,0,1,0,-2,1,
==> 0,0,0,1,1,-2
==> [2]:
==> 0,0,0,0,0,0
==> [3]:
==> [1]:
==> [1]:
==> 2,1,1
==> [2]:
==> 4,1,1
==> [2]:
==> [1]:
==> 2,1,2
==> [2]:
==> 4,1,2
==> [3]:
==> [1]:
==> 4,2,1
==> [2]:
==> 6,2,1
==> [4]:
==> [1]:
==> 4,2,2
==> [2]:
==> 6,2,2
==> [5]:
==> [1]:
==> 6,3,1
==> [2]:
==> 7,3,1
==> [6]:
==> [1]:
==> 6,3,2
==> [2]:
==> 7,3,2
==> [4]:
==> 1,1,1,1,1,1
// The output is a list whose first entry contains the intersection matrix
// of the exceptional divisors. The second entry is the list of genera
// of these divisors. The third and fourth entry contain the information
// how to find the corresponding divisors in the respective charts.
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