Extremal contractions from 4-dimensional manifolds to 3-folds

Abstract

Let $g:X\to Y$ be the contraction of an extremal ray of a smooth projective 4-fold $X$ such that $\dim Y=3$. Then $g$ may have a finite number of 2-dimensional fibers. We shall classify those fibers. Especially we shall prove that any two points of such a fiber is joined by a chain of rational curves of length at most 2 with respect to $-K_X$, and that $|-K_X|$ is $g\text{-free}$.

65 pages, TeX dialect: amsppt

References in corpus (1)

• Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic

Cited by in corpus (8)

• On Contractions of smooth varieties
• The rationality problem for conic bundles
• On covering and quasi-unsplit families of rational curves
• On the second exterior power of tangent bundles of Fano fourfolds with Picard number $rho(X)geqslant2$
• Fano threefolds
• On the birational geometry of Fano 4-folds
• Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants
• On Classification of the extremal contraction from a smooth fourfold