Pluricanonical maps for threefolds of general type
Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1315-1330.

In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.

Nous prouvons que pour une variété de dimension 3 de type général et de grand volume le second plurigenre est positif et la cinquième application canonique est birationnelle

DOI: 10.5802/aif.2295
Classification: 14J30,  14E05
Keywords: Threefolds, pluricanonical maps, extension theorems
Todorov, Gueorgui Tomov 1

1 University of Utah Dep. of mathematics, JWB 107 155 S 1400 E RM 233 Salt Lake City TU 84112-0090 (USA)
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Todorov, Gueorgui Tomov. Pluricanonical maps for threefolds of general type. Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1315-1330. doi : 10.5802/aif.2295. http://www.numdam.org/articles/10.5802/aif.2295/

[1] J. Chen and M. Chen and D. Zhang The 5-canonical system on 3-folds of general type (math.AG/0512617)

[2] Ambro, F. The locus of log canonical singularities (arXiv:mathAG/9806067)

[3] Benveniste, X. Sur les applications pluricanoniques des variété de type très général en dimension 3, Amer J. Math, Volume 108 (1986), pp. 433-449 | DOI | MR | Zbl

[4] Bombieri, E. Canonical models of surfaces of general type, Inst. Hautes Études Sci. Publ., Volume 42 (1973), pp. 171-219 | DOI | Numdam | MR | Zbl

[5] C. Hacon and J. McKernan Boundedness of pluricanonical maps of varieties of general type (arXiv:math.AG/0504327, to appear in Inv. Math) | Zbl

[6] Chen, M. On pluricanonical maps for threefolds of general type, J.Math. Soc. Japan, Volume 50 (1998), pp. 615-621 | DOI | MR | Zbl

[7] J. Chen and C. Hacon Linear series of irregular varieties, World Scientific Press, Japan, 2002 | MR | Zbl

[8] Kawamata, Y. On the extension problem of pluricanonical forms, Contemp. Math, Volume 241 (199), pp. 193-207 | MR | Zbl

[9] Kawamata, Y. On Fujita’s freeness conjecture for 3-folds and 4-folds, Math. Ann., Volume 308 (1997), pp. 893-899 | DOI | Zbl

[10] McKernan, J. Boundedness of log terminal Fano pairs of bounded index (arXiv:math.AG/0205214 v1)

[11] Kollár, J. Higher direct images of sheaves I, Ann. of Math, Volume 127 (1988), pp. 93-163

[12] Kollár, J. Shafarevich maps and automorphic forms, M. B. Porter Lectures, Princeton University Press, Princeton, NJ, 1995 | MR | Zbl

[13] Kollár, J.; Mori, S. Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[14] Lazarsfeld, Robert Positivity in algebraic geometry. II, Springer-Verlag, Berlin, 2004 | MR | Zbl

[15] Lee, S. Quint-canonical systems on canonical threefolds of index 1, Comm. Algebra, Volume 28 (2000), pp. 5517-5530 | DOI | MR | Zbl

[16] Takayama, S. Pluricanonical systems on algebraic varieties of general type (preprint, to appear in Inv. Math.) | Zbl

[17] Tsuiji, H. Pluricanonical systems of projective varieties of general type (arXiv:math.AG/9909021)

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