(numList,adjList,ptsList,J)=adjointMatrix(I)
(numList,adjList,ptsList,J)=adjointMatrix(I,N)
Adjunction determines the image X' of X under the morphism phi: X > X' defined by H+K. By Sommese and Van de Ven [SVdV] H+K is birational and blows down presisely all (1) lines of unless
(1) X is a P2 linearly or quadratically embedded, or ruled in lines,
(2) X is a anticanonical embedded Del Pezzo surface,
(3) X is a conic bundle in which case phi_{H+K}: X > B maps X to a curve B and the fibers are conics, or
(4) X is an element of one of the four families of exceptions where K+H defines a finite to 1 map. See TO "specialFamiliesOfSommeseVandeVen".
Since a (1) conic on X become (1) line on X', repeating this process finally reaches a minimal surface unless X has negative Kodaira dimension.
In case X is a rational surface, and the lucky case that the final surface is P2, one can use the list adjList to get a rational parametrization.
In case one ends up with a del Pezzo surface or a conic bundle, one has to identify the exceptional lines, thus one might need an algebraic field extension, to get a rational parametrization. However, one can always parametrize X in terms of the final surface in the adjunction process.
The numerical data are collected in a list with an entry
(n,d,pi)= (dim Pn_i, degree X_i, sectional genus of X_i)
for each surface X_i in the adjunction process, starting with X=X_0 and an entry the integer k if X_i > X_(i+1) blows down k (1) lines.


















The object adjunctionProcess is a method function.