next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Cremona :: exceptionalLocus

exceptionalLocus -- exceptional locus of a birational map



This method simply calculates the inverse image of the base locus of the inverse map, which in turn is determined through the method inverse.

Below, we compute the exceptional locus of the map defined by the linear system of quadrics through the quintic rational normal curve in $\mathbb{P}^5$.

i1 : P5 := ZZ/100003[x_0..x_5];
i2 : phi = rationalMap(minors(2,matrix{{x_0,x_1,x_2,x_3,x_4},{x_1,x_2,x_3,x_4,x_5}}),Dominant=>2);

o2 : RationalMap (quadratic rational map from PP^5 to 5-dimensional subvariety of PP^9)
i3 : E = exceptionalLocus phi;

o3 : Ideal of ------[x ..x ]
              100003  0   5
i4 : assert(E == phi^* ideal phi^-1)
i5 : assert(E == minors(3,matrix{{x_0,x_1,x_2,x_3},{x_1,x_2,x_3,x_4},{x_2,x_3,x_4,x_5}}))

See also

Ways to use exceptionalLocus :

For the programmer

The object exceptionalLocus is a method function with options.