「極小モデル」の版間の差分

 

The first key result is the [[Cone of curves|Cone theorem]] of [[Shigefumi Mori|Mori]], describing the structure of the cone of curves of <math>X</math>. Briefly, the theorem shows that starting with <math>X</math>, one can inductively construct a sequence of varieties <math>X_i</math>, each of which is 'closer' than the previous one to having <math>K_{X_i}</math> nef. However, the process may encounter difficulties: at some point the variety <math>X_i</math> may become 'too singular'. The conjectural solution to this problem is the [[Flip (algebraic geometry)|flip]], a kind of codimension-2 surgery operation on <math>X_i</math>. It is not clear that the required flips exist, nor that they always terminate (that is, that one reaches a minimal model <math>X'</math> in finitely many steps.) {{harvtxt|Mori|1988}} showed that flips exist in the 3-dimensional case; much recent work has focused on existence and termination problems in higher dimensions.-->

 

==参考文献==