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Inversion of adjunction on log canonicity

Masayuki Kawakita
- 24 Aug 2006 - 
- Vol. 167, Iss: 1, pp 129-133
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TLDR
In this paper, the authors prove inversion of adjunction on log canonicity, and prove that adjunction is invertible on log canonicity, but not on log-canonicity.
Abstract
We prove inversion of adjunction on log canonicity.

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Stable maps in higher dimensions

TL;DR: In this article, the authors formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point.
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Polystable log Calabi-Yau varieties and Gravitational instantons

TL;DR: In this paper, the authors consider a good proper subclass of Calabi-Yau manifolds, which they regard as certain poly-stable ones, morally corresponding to semistable with closed (minimal) orbits, as the classical analogue of GIT.
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On the properness of the moduli space of stable surfaces

TL;DR: The moduli spaces of stable surfaces serve as compactifications of the modulus spaces of canonical models of smooth surfaces in the same way the moduli space of stable curves compactify the modulo spaces of smooth curves as mentioned in this paper.
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Vanishing and Semipositivity Theorems for Semi-log Canonical Pairs

TL;DR: In this article, a vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs over curves was proved, which implies the projectivity of the moduli spaces of stable varieties.
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Base change behavior of the relative canonical sheaf related to higher dimensional moduli

TL;DR: In this article, the compatibility of the relative canonical sheaf with base change fails generally in families of normal varieties, and it always fails if the general fiber of a family of pure dimension n is Cohen-Macaulay and the special fiber contains a strictly S n-1} point.
References
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Book

Birational Geometry of Algebraic Varieties

TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
Journal Article

Flips and Abundance for Algebraic Threefolds

János Kollár
- 01 Jan 1992 - 
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