A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume
Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2043-2082.

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove some optimal results in dimensions 4 and 5, which are parallel to some well-known results on surfaces and 3-folds.

Nous étudions l’indice de stabilité canonique d’une variété projective lisse de type général avec un grand volume canonique ou un grand genre géométrique. Comme applications d’un théorème général d’extension établi dans la première partie, nous prouvons des résultats optimaux en dimensions 4 et 5 similaires à certains résultats bien connus sur les surfaces et les variétés de dimension 3.

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DOI: 10.5802/aif.3129
Classification: 14E05, 14J35, 14J40
Keywords: canonical volumes, pluricanonical systems, extension theorems
Mot clés : volumes canoniques, systèmes pluricanoniques, théorèmes d’extension
Chen, Meng 1; Jiang, Zhi 2

1 School of Mathematical Sciences & Shanghai Centre for Mathematical Sciences Fudan University, Shanghai 200433 (China)
2 Département de Mathématiques Bâtiment 425, Université Paris-Sud 91405 Orsay (France)
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Chen, Meng; Jiang, Zhi. A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume. Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2043-2082. doi : 10.5802/aif.3129. http://www.numdam.org/articles/10.5802/aif.3129/

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