Boundedness of canonical Q-Fano 3-folds

By J. Kollár, Y. Miyaoka, S. Mori. 2000

105 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e72f1cafb234752b1a684300745a3d17ccaf9e05

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Citations in the corpus

Anti-pluricanonical systems on Fano varieties (2016, background): “The conjecture was previously known in dimension two [3], for smooth X [34], for toric X [11], for threefolds of Picard number one and terminal singularities [27], for threefolds with canonical singularities [35], in dimension three with KX having bounded Cartier index [10], in any dimension with KX”
Threefold thresholds (2003, background): “Kawamata [15] proved (3.7) for Fano threefolds with Picard number one and terminal singularities and Kollár, Miyaoka, Mori and Takagi [21] proved that all Fano threefolds with canonical singularities are bounded.”
Simple finite subgroups of the Cremona group of rank 3 (2009, background): “The orbifold Riemann-Roch and Myaoka-Bogomolov inequality give us (see [Kaw92], [KMMT00]) 4”
Jordan property for groups of birational selfmaps (2013, background): “Note that Conjecture BAB is proved in dimension n 6 3 (see [KMMT00]).”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “ndex r > 1 and let P1,...,Pl be its G-orbit. Here l = pt for some t with t ≥ s − 3 (see Lemma 2.4). By the orbifold Riemann-Roch formula [Rei87] and a form of Bogomolov-Miyaoka inequality [Kaw92], [KMMT00] we have X rP i − 1 rP i < 24. 8 Since ri − 1/ri ≥ 3/2, we have 3l/2 < 24 and so ps−3”
Jordan groups and automorphism groups of algebraic varieties (2013, background): “[24], the answer to Question 8 is affirmative also in each of the following cases:”
Singularities of linear systems and boundedness of Fano varieties (2016, background): “Boundedness was known for: Fano 3-folds with terminal singularities and Picard number one [18], Fano 3-folds with canonical singularities [23], Fano 3-folds with fixed Cartier index of KX [6], and more generally, Fano varieties of given dimension with fixed Cartier index of KX [11]; in a given dimen”
On Quasismooth Weighted Complete Intersections (2009, unknown): “On the other hand, by [14], we have −KX · c2(X) ≥ 0.”
Jordan property for Cremona groups (2012, background): “Note that Conjecture 1.7 is settled in dimension 3 (see [23]), so we have the following C OROLLARY 1.9.”
Birational Geometry of 3-fold Mori Fibre Spaces (2003, background): “These are in turn parametrised by weak terminal Fano 3-folds of rank 2, and these are bounded by [KMMT00].”