Inversion of adjunction on log canonicity

By M. Kawakita. 2005

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We prove inversion of adjunction on log canonicity.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1c90112e22ad6fac682d2cdf3b90562b9e93cf79

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In Computational Theory and Mathematics

Citations in the corpus

A minimizing valuation is quasi-monomial (2019, unknown): “= vi(hi). This implies that KY i +Si +µ−1 i∗ ( 1 N Φi +∆i) |S i = µ∗ i (KX +∆+ 1 Φi)|S i = µ∗ i (KX +∆+ 1 N Ψi)|S i = KS i +∆+ Si . Since (Si,∆+ Si ) is log canonical, by inversion of adjunction (see [Kaw07]), we know that (Yi,Si + µ −1 i∗ (Φi + ∆i)) is log canonical along Si, which implies that (X,”
Moduli of varieties of general type (2010, background): “anonical rings are not always ﬁnitely generated [Kol07]. It is a quite subtle theorem that semi log canonical models actually satisfy the preliminary deﬁnion (7.5). This is proved in [K+92, 17.4] and [Kaw07]. To get a feeling for semi log canonical, let us review the classiﬁcation of slc surface sin”
On a generalized canonical bundle formula and generalized adjunction (2018, background): “In the case that W has codimension 1, the statement takes the following simpler form, originally due to Kawakita [26].”
Singularities of linear systems and boundedness of Fano varieties (2016, background): “This follows from inversion of adjunction [16], if we show KS +B + S = (KX +B +)|S which is equivalent to showing R|S = RS .”
Introduction to the log minimal model program for log canonical pairs (2009, methodology): “separates x1 and x2. The key points of the proofs of Theorems 4.48 and 4.49 are the vanishing theorem (see Theorem 3.39 (ii)) and the inversion of adjunction on log canonicity (see Corollary 4.47 and [Kw]). The ﬁnal theorem in this book is a generalization of Koll´ar’s eﬀective base point freeness (”
Jet schemes and singularities (2006, background): “cs (see Theorem 7.9 for the precise statement). We apply this point of view to give a proof of the following version of Inversion of Adjunction. This has been proved independently also by Kawakita in [Kaw2]. Theorem 1.1. Let Abe a nonsingular variety and Y = Ps i=1 qiYi, where the qi are non-negativ”
Which powers of holomorphic functions are integrable (2008, methodology): “e formal power series case). All these results were proved in the algebraic and analytic settings. The methods are either analytic, or, as the proofs of inversion of adjunction in [Kol92, Sec.17] and [Kaw07], rely ultimately on a relative version of the Kodaira vanishing theorem. This vanishing is k”
Log canonical singularities are Du Bois (2009, background): “, if φ: X→ Bis a family with potentially lc ﬁbers, Bis a smooth curve and there exists an effective Q-divisor such that KX+Dis Q-Cartier andD Xb = Dbthen φis an lc morphism by inversion of adjunction [Kaw07]. Furtherobservethat if φ: (X,D) → Bis an lc morphism,then for anyb∈ B, choosing (Y,∆) = (X,D”
F-adjunction (2009, background): “Furthermore, in characteristic zero, the singularities of (X, D +1) near D are closely related to the singularities of (D,1D) [Kollár et al. 1992; Kawakita 2007].”
Globally F-regular and log Fano varieties (2009, background): “canonical if and only if it is log canonical in a neighborhood of m, and this holds if and only if (Y; Y+X) is log canonical in a neighborhood of X. Finally, inversion of adjunction on log canonicity [Kaw07] implies this holds if and only if, restricting to X, the pair (X; Yj X) = (X;) is log canoni”
Anti-pluricanonical systems on Fano varieties (2016, background): “This centre is also a non-klt centre of (X,B + G + f∗D), hence intersecting it with G gives a non-klt centre of (G,BG+ g ∗C) mapping onto C, by inversion of adjunction [24].”
Testing log K-stability by blowing up formalism (2011, background): “Consult [12, section 5.2], [11], [22, Corollary 1.2] for the details and proofs.”
Shokurov's ACC conjecture for log canonical thresholds on smooth varieties (2009, methodology): “have lct(b) = lct(a). This result (for principal ideals) was ﬁrst proven by Koll´ar in [Kol2] using deep results in the Minimal Model Program from [BCHM] and a theorem on Inversion of Adjunction from [Kaw]. We give an elementary proof of Theorem 1.4 which only uses the Connectedness Theorem of Shoku”
Simple finite subgroups of the Cremona group of rank 3 (2009, background): “Write 0 ∼ ν(KX+S) = KS′+D, where D is the different, see [Sho93], [Kaw07].”