Some remarks on the study of good contractions
Let \(X\) be a complex projective variety with log terminal singularities. A good contraction is a map \(\varphi: X\to Z\) onto a normal variety with connected fibres, such that the \(\mathbb{Q}\)-canonical divisor \(-K_X\) is \(\varphi\)-ample. In this case there exist a \(\varphi \)-ample line bundle \(L\) and a rational number \(r\) such that \(K_X + rL\) is the pullback of a line bundle of \(Z\). In this note the author studies the structure of \(\varphi\), proving in particular that for any fiber \(F:\) \(\dim F \geq r-1\) (and \(\dim F \geq r\) if \(\varphi\) is birational).
scientific article; zbMATH DE number 784080
scientific article