On pluricanonical systems of algebraic varieties of general type
By Meng Chen. 2008
155 citations recorded by the source corpus.
We extend Kollar's technique to look for an explicit function h(n) with phi_m birational onto its image for all integers $m\geq h(n)$ and for all n-dimensional nonsingular projective varieties of general type.
View Paper: https://www.semanticscholar.org/paper/ebfa74afa7b845d6625e2f428fb1c370719d974b
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Citations in the corpus
- Singularities on normal varieties (2008, methodology): “Proof. If � is an m-compatible boundary for (X, Z + H) for a sufficiently divisiblem, then J(X, Z) = J((X,�); Z) and adjH(X, Z) = adjH((X,�); Z). Therefore the result follows from the log Q-Gorenstein case, in which case it is well known (see, for example, the arguments in [ Tak , Proposition 2.4]).”
- Differentiability of volumes of divisors and a problem of Teissier (2006, unknown): “tion of pseudo-effectivity of [BDPP]. In a similar vein, the proof of Theorem B is based on a suitable generalization of Fujita’s theorem for restricted volumes, obtained independently in [ELMNP3] and [Ta]. If D ⊂X is a prime divisor on the smooth projective variety, we say that a line bundle L is D-”
- 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].”
- Bergman kernels and the pseudoeffectivity of relative canonical bundles (2007, methodology): “Rather than reproducing here his arguments, we will use a more direct approach taken from [26] (see also the papers [8], [28] and [34] for other variations and further results on this theme).”
- Explicit birational geometry of threefolds of general type (2007, background): “[29] S. Takayama, Pluricanonical systems on algebraic varieties of general type, Invent.”
- Extension theorems, non-vanishing and the existence of good minimal models (2010, result): “The above theorem is a strong generalization of similar results available in the literature (see for example [Siu98], [Siu00], [Takayama06], [Takayama07], [HM07], [Paun07], [Claudon07], [EP07], [dFH09], [Var08], [Paun08], [Tsuji05], [HM10], [BP10]).”
- The Minimal Model Program revisited (2012, result): “ a slight generalization of the lifting theorem by Hacon-McKernan [HM10], which is itself a generalization of results by Siu [Siu98, Siu02] and Kawamata [Kaw99]. Similar results were also obtained in [Tak06], [Pa˘u07] and [EP10]. Theorem 3.3. Let Xbe a smooth projective variety, let Sbe a prime divi”
- Semipositivity theorems for moduli problems (2012, methodology): “first constructed in the category of algebraic spaces (cf. [KM]). As a corollary of Theorem 1.1, by using the boundedness result obtained through works of Tsuji, Hacon–McKernan and Takayama (cf. [HM], [T]), we have: Corollary 1.2 (cf. [K1, 5.6. Corollary], [Kr, Corollary 1.2], and [AH, Proposition 6.”
- Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs (2014, background): “2: • when dim W = 2 [12], • when κ(W) = 1 [7], • when W is of general type [8, 21] (see also [23]),”