A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume
[Une réduction de l’indice de stabilité canonique des variétés projectives des dimensionnelles 4 et 5 à grand volume]
Annales de l'Institut Fourier, Tome 67 (2017) no. 5, pp. 2043-2082.

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.

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.

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DOI : https://doi.org/10.5802/aif.3129
Classification : 14E05,  14J35,  14J40
Mots clés : volumes canoniques, systèmes pluricanoniques, théorèmes d’extension
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     author = {Chen, Meng and Jiang, Zhi},
     title = {A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume},
     journal = {Annales de l'Institut Fourier},
     pages = {2043--2082},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {67},
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     year = {2017},
     doi = {10.5802/aif.3129},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.3129/}
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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, Tome 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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