On extremal contractions from threefolds to surfaces: The case of one non-Gorenstein point and a nonsingular base surface (Q1807493)

This paper continues the author's study of the local structure of extremal contractions \(f: X \rightarrow S\) from a complex threefold \(X\) with only terminal singularities onto a surface \(S\). Especially let \(f\) be a Mori conic bundle (see definition 0.1). Then the main result (theorem 3.1) shows that if \(S\) is non-singular and \(X\) has a unique non-Gorenstein point \(P\), then the general member of some of the systems \(|-nK_X|\), \(n = 1,2,3\), does not contain the fiber of \(f\) through the point \(P\).