Quasi-log varieties

Abstract

We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.

LaTex, 24 pages; title and terminology has been changed; new adjunction statement (4.9). to appear in Proc. of Steklov Institute, vol 240

References in corpus (1)

• Base point free theorem of Reid-Fukuda type

Cited by in corpus (27)

• Introduction to the log minimal model program for log canonical pairs
• Poles of maximal order of motivic zeta functions
• An Injectivity Theorem
• The dual complex of singularities
• Singular semipositive metrics in non-Archimedean geometry
• Introduction to the theory of quasi-log varieties
• Vanishing and injectivity theorems for LMMP
• Simple normal crossing Fano varieties and log Fano manifolds
• On Finiteness of B-representation and Semi-log Canonical Abundance
• Adjoint rings are finitely generated
• Higher direct images of log canonical divisors and positivity theorems
• On the anti-canonical ring and varieties of Fano type
• On the semiampleness of the positive part of CKM Zariski decompositions
• Quasi-log canonical pairs are Du Bois
• Fano varieties with large Seshadri constants
• Regularity, singularities and $h$-vector of graded algebras
• Vanishing theorems for toric polyhedra
• Dual complex of log Fano pairs and its application to Witt vector cohomology
• Notes on the log minimal model program
• The dualizing complex of $F$-injective and Du Bois singularities
• Supplement to the paper "On existence of log minimal models II"
• Letters of a Bi-Rationalist: VII. Ordered termination
• Introduction to the Minimal Model Program and the existence of flips
• M-regular Decompositions for pushforwards of pluricanonical bundles of pairs to abelian varieties
• Degenerations of log Hodge de Rham spectral sequences, log Kodaira vanishing theorem in characteristic $p>0$ and log weak Lefschetz conjecture for log crystalline cohomologies
• Note on characterizations of projective spaces
• Remarks on very basic slc-trivial fibrations