Boundedness of pluricanonical maps of varieties of general type

By Christopher D. Hacon, J. McKernan. 2005

232 citations recorded by the source corpus.

Using the techniques of [20] and [10], we prove that certain log forms may be lifted from a divisor to the ambient variety. As a consequence of this result, following [22], we show that: For any positive integer n there exists an integer rn such that if X is a smooth projective variety of general type and dimension n, then $\phi_{rK_X}\colon X\dasharrow\mathbb{P}(H^0(\mathcal{O}_{X}(rK_X)))$ is birational for all r≥rn.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6f454493224debff9efbd0a65b01f3d052c6ad5f

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Bergman kernels and the pseudoeffectivity of relative canonical bundles (2007, background): “[16], [28] and also the paragraph 3 of this article).”
Boundedness of log Calabi–Yau pairs of Fano type (2014, background): “cally known that for curves m≥ 3 suﬃces and for surfaces m≥ 24 suﬃces (in fact by work of Bombieri, if Xis of general type, then m≥ 5 is suﬃcient). This leads to the following natural conjecture (cf. [HM06]). Conjecture 1.1. Fix a positive integer n. Then there exists an integer k, which only depend”
PLURICANONICAL SYSTEMS ON PROJECTIVE VARIETIES OF GENERAL TYPE (2007, methodology): “The analogous result in [ HM ] is Corollary 3.17.”
Explicit birational geometry of threefolds of general type (2007, background): “Notice that a recent remarkable result of Hacon and McKernan [15], Takayama [29] and Tsuji [31] implies the affirmative answer to both Problems.”
On pluricanonical systems of algebraic varieties of general type (2008, background): “The existence of rn for varieties of general type was proved by Hacon-Mkernan [10], Takayama [19] and Tsuji [20] and, recently, r3 ≤ 73 was proved by Chen-Chen [6, Theorem 1.”
Anti-pluricanonical systems on Fano varieties (2016, background): “If KX is ample, then there is m depending only on the dimension such that |mKX | defines a birational embedding into some projective space, by Hacon-McKernan [15] and Takayama [45].”
Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014, background): “1: • when dimW = 2 [10], • when κ(W ) = 1 [6], • when W is of general type [7][17], • when κ(W ) = 2 [19] (see also [18]), • when X is non-uniruled, V → X has maximal variation and its general fibres have good minimal models [15](see also [5]), • when V → X has zero variation and its general fibres ”
Existence of minimal models for varieties of log general type (2006, unknown): “f [2], (1.2) completes the proof of (1.1). The main ideas used in this paper have their origins in the work of Shokurov on the existence of ﬂips [10] together with the use of the extension theorem of [4] which in turn was inspired by the work of Kawamata, Siu and Tsuji (cf. [6], [12] and [15]). For ”