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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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