Mori conic bundles with a reduced log-terminal boundary

Abstract

We study the local structure of Mori contractions f : X → Z of relative dimension one under an additional assumption that there exists a reduced divisor S such that K X + S is plt and anti-ample.

On Semistable Mori Conic Bundles

“…Proof. If K S + C is plt, then S has two singularities of types 1 n (1, q) and 1 n (1, n− q) (see [7,Theorem 2.5]). If they are of type T, then (q + 1) 2 ≡ 0 mod n, (n − q + 1) 2 ≡ 0 mod n.…”

“…In this paper, we propose a method of construction of examples of Mori contractions from threefolds to surfaces (see [6][7][8]). We refer the reader to [3,5] for the terminology of the minimal model theory.…”