Threefolds with Kodaira Dimension 0 or 3

Ezio Stagnaro

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 1149-1182
  • ISSN: 0392-4041

Abstract

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Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in ℙ 4 , having the irregularities q 1 = q 2 = 0 and the following periodical sequences of plurigenera respectively ( p g , P 2 , P 3 , … , P m , … ) = ( 0 , 0 , 1 , 0 , 0 , 1 , … ) , ( 0 , 0 , 0 , 1 , 0 , 0 , 0 , 1 , … ) , ( 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 1 , … ) . In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with q ⁢ q 1 = q 2 = 0 , p g = 1 , P 2 = 2 whose m-canonical transformation is birational if and only if m ≥ 11 .

How to cite

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Stagnaro, Ezio. "Threefolds with Kodaira Dimension 0 or 3." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 1149-1182. <http://eudml.org/doc/290383>.

@article{Stagnaro2007,
abstract = {Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in $\mathbb\{P\}^4$, having the irregularities $q_1=q_2= 0$ and the following periodical sequences of plurigenera respectively \begin\{equation*\}(p\_g,P\_2, P\_3, \ldots, P\_m, \ldots) = (0, 0, 1, 0, 0, 1,\ldots),(0, 0, 0, 1, 0, 0, 0, 1, \ldots), (0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots).\end\{equation*\}In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with $qq_1 = q_2 = 0, p_g =1$, $P_2=2$ whose m-canonical transformation is birational if and only if $m \geq 11$.},
author = {Stagnaro, Ezio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {1149-1182},
publisher = {Unione Matematica Italiana},
title = {Threefolds with Kodaira Dimension 0 or 3},
url = {http://eudml.org/doc/290383},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Stagnaro, Ezio
TI - Threefolds with Kodaira Dimension 0 or 3
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 1149
EP - 1182
AB - Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in $\mathbb{P}^4$, having the irregularities $q_1=q_2= 0$ and the following periodical sequences of plurigenera respectively \begin{equation*}(p_g,P_2, P_3, \ldots, P_m, \ldots) = (0, 0, 1, 0, 0, 1,\ldots),(0, 0, 0, 1, 0, 0, 0, 1, \ldots), (0, 0, 0, 0, 1, 0, 0, 0, 0, 1, \ldots).\end{equation*}In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with $qq_1 = q_2 = 0, p_g =1$, $P_2=2$ whose m-canonical transformation is birational if and only if $m \geq 11$.
LA - eng
UR - http://eudml.org/doc/290383
ER -

References

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  8. RONCONI, M. C., A threefold of general type with q 1 = q 2 = p g = P 2 = 0 , Proc. Monodromy Conference, Steklov Institute, Moscow, June 25-30, 2001, Acta Appl. Mathematicae, 75 (2003), 133-150. Zbl1051.14047MR1975564DOI10.1023/A:1022336011727
  9. STAGNARO, E., Adjoints and pluricanonical adjoints to an algebraic hypersurface, Annali di Mat. Pura ed Appl., 180 (2001), 147-201. Zbl1072.14044MR1847403DOI10.1007/s10231-001-8201-6
  10. STAGNARO, E., Pluricanonical maps of a threefold of general type, Proc. Greco Conference, Catania, "Le Matematiche", Vol. LV (2000) - Fasc. II, 533-543. Zbl1072.14045MR1984218
  11. UENO, K., Birational Geometry of Algebraic Threefolds, Journées de géométrie algébriques d'Angers 1979, Sijthoff and Noordhoff1980, 311-323. MR605349

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