On extremal rays of the higher dimensional varieties

DOI10.1007/BF01389057zbMath0554.14001MaRDI QIDQ759806

Tetsuya Ando

Publication date: 1985

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143259

zbMATH Keywords

exceptional setextremal raysbirational contractionnot numerically effective canonical divisor

Mathematics Subject Classification ID

Rational and birational maps (14E05) Families, moduli, classification: algebraic theory (14J10) Divisors, linear systems, invertible sheaves (14C20) (n)-folds ((n>4)) (14J40)

Related Items (40)

A footnote to a paper by Ionescu ⋮ On d-folds whose canonical bundle is not numerically effective, according to Mori and Kawamata ⋮ Fano varieties with large Seshadri constants in positive characteristic ⋮ Remarks on nef and movable cones of hypersurfaces in Mori dream spaces ⋮ The rationality problem for conic bundles ⋮ Small contractions of four dimensional algebraic manifolds ⋮ Derived categories of Artin-Mumford double solids ⋮ Alcuni risultati sulla classificazione delle varieta’ algebriche a piu’ dimensioni ⋮ Classification of Fano manifolds containing a negative divisor isomorphic to projective space ⋮ Amplified endomorphisms of Fano fourfolds ⋮ Classification of ℚ-Fano 3-folds of Gorenstein index 2 via key varieties constructed from projective bundles ⋮ A note on flatness of some fiber type contractions ⋮ The Lefschetz defect of Fano varieties ⋮ Duality related with key varieties of \(\mathbb{Q} \)-Fano threefolds constructed from projective bundles ⋮ Trisecant flops, their associated \(K3\) surfaces and the rationality of some cubic fourfolds ⋮ Residual categories of quadric surface bundles ⋮ On the minimal length of extremal rays for Fano four-folds ⋮ On cylindrical smooth rational Fano fourfolds ⋮ A note on the Picard number of singular Fano 3-folds ⋮ Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category ⋮ Non-elementary Fano conic bundles ⋮ Cylinders in Fano varieties ⋮ Uniruled varieties with split tangent bundle ⋮ Extremal rays on higher dimensional projective varieties ⋮ On the homeomorphism type of smooth projective fourfolds ⋮ Fano manifolds obtained by blowing up along curves with maximal Picard number ⋮ On Fano manifolds, which are P^K-bundles over P² ⋮ On structure of small contractions of odd dimensional projective varieties ⋮ A remark on Fano 4-folds having \((3,1)\)-type extremal contractions ⋮ The structure of uniruled manifolds with split tangent bundle ⋮ Sur des variétés de Moishezon dont le groupe de Picard est de rang un ⋮ Fano 4-Folds with scroll structure ⋮ Extremal contractions from 4-dimensional manifolds to 3-folds ⋮ Relative linear extensions of sextic del Pezzo fibrations over curves ⋮ Pseudo-index of Fano manifolds and smooth blow-ups ⋮ Unnamed Item ⋮ When \(K+(n-4)L\) fails to be nef ⋮ Complex manifolds whose blow-up at a point is Fano ⋮ A note on nonvanishing and applications ⋮ Examples of cylindrical Fano fourfolds

Cites Work

• The cone of curves of algebraic varieties
• The cone theorem: Note to a paper of Y. Kawamata
• Classification of projective varieties of \(\Delta\)-genus one
• On the structure of polarized manifolds with total deficiency one. I
• Normal Gorenstein surfaces with ample anti-canonical divisor
• On the inverse of monoidal transformation
• THE NONVANISHING THEOREM
• FANO 3-FOLDS. I
• Threefolds whose canonical bundles are not numerically effective

This page was built for publication: On extremal rays of the higher dimensional varieties