A CANONICAL BUNDLE FORMULA

By O. Fujino, S. Mori. 2000

191 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4827c17f0bdd0a65489faa400bec6e22fd768500

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Citations in the corpus

PLURICANONICAL SYSTEMS ON PROJECTIVE VARIETIES OF GENERAL TYPE (2007, methodology): “For 3-folds of Kodaira dimension 1, as a by product of their canonical bundle formula, Fujino and Mori have proved in [ FM ] the existence of an eectively computable number m3 such that ’m3 yields the Iitaka fibration.”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, background): “forward application of theorem C. Corollary 1.9. If X is nonsingular projective of general type, then the canonical ring R(X,KX) is ﬁnitely generated. Remark 1.10. In fact, by work of Fujino and Mori [FM00], the results here imply the stronger statement that if X is nonsingular, then the canonical r”
Introduction to the log minimal model program for log canonical pairs (2009, methodology): “ing R(X/S,KX +B) = M m≥0 f∗OX(xm(KX +B)y) is a ﬁnitely generated OS-algebra. When (X,B) is klt, we can reduce Conjecture 3.10 to the case when KX + B is f-big by using a canonical bundle formula (see [FM]). Thus, Conjecture 3.10 holds for klt pairs by [BCHM]. When (X,B) is lc but not klt, we do not ”
Boundedness of log Calabi–Yau pairs of Fano type (2014, methodology): “eral type case (cf. [HMX13,HMX14]). However, the case of intermediate Kodaira dimension is more complicated and very little is known in arbitrary dimension. The well-known strategy, ﬁrst developed in [FM00], is to use the canonical bundle formula, which is a far reaching generalization of Kodaira’s ”
Shokurov's Boundary Property (2002, background): “This type of fibrations appear naturally in higher codimensional adjunction [14, 15, 1] and in the study of parabolic fiber spaces [ 6 , 5]. We refer the reader to Remark 2.2 for examples where the technical assumption (2) is satisfied, and to Section 1 for the definition of Shokurov’s discrepancy b”
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014, methodology): “Applying the canonical bundle formula of [7] (which is based on [16]), perhaps after replacing W and X birationally, there is a Qboundary B and a nef Q-divisor M on X such that for any natural number m divisible by bF we have a natural isomorphism between H(W,mKW) and H(X,m(KX + B + M)).”
On a generalized canonical bundle formula and generalized adjunction (2018, methodology): “This kind of pair arises naturally in certain situations, such as the canonical bundle formula [27, 3, 18], and adjunction theory [27, 3, 5].”
The moduli b-divisor of an lc-trivial fibration (2003, background): “1 in case the generic fibre Xη has canonical singularities and Bη = 0 (see Fujino, Mori [4, 5], or [3]).”
Existence of minimal models for varieties of log general type (2006, unknown): “This program was successfully completed for 3-folds in the 1980s by the work of Kawamata, Kollár, Mori, Reid, Shokurov and others.”
Existence of log canonical closures (2011, methodology): “presentation. 2.1. Canonical bundle formula. In this subsection, we will give a version of the canonical bundle formula that follows from the work of Kawamata, FujinoMori and Ambro (cf. [Kawamata98], [FM00], [Ambro04] and [Koll´ar07]). 6 CHRISTOPHERD.HACONANDCHENYANGXU Theorem 2.1. Let (X,∆) be a dl”
The Minimal Model Program revisited (2012, result): “l crossings and ⌊∆⌋ = 0, the ring R(X,KX + ∆) is ﬁnitely generated. As in the higher dimensional case, see [BCHM10] and [CL10a], by the existence of log resolutions and by a result of Fujino and Mori [FM00], we may and will assume, without loss of generality, that the divisor ∆ can be written as ∆ =”
On Zariski decomposition problem (2002, background): “Later the last fact was generalized in [6]:”