Abstract
In this paper we prove that if X is an irregular 3-fold with χ(ω X ) > 0, then |mK X | is birational for all m ≥ 5.
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References
Atiyah M. (1957) Vector bundles over an elliptic curves. Proc. London Math. Soc. 7, 414–452
Bombieri E. (1973) Canonical models of surfaces of general type. Inst. Hautes Études Sci. Publ. Math. 42, 171–219
Chen J.A., Hacon C.D. (2002) Linear series of irregular varieties. In: Algebraic Geometry in East Asia, Japan, World Scientific Press
Chen J.A., Hacon C.D. (2002) On algebraic fiber spaces over varieties of maximal Albanese dimension. Duke Math. J. 111, 159–175
Fujita T. (1978) On Kähler fiber spaces over curves. J. Math. Soc. Japan 30(4): 779–794
Green M., Lazarsfeld R. (1987) Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville. Invent. Math. 90, 389–407
Green M., Lazarsfeld R. (1991) Higher obstructions to deforming cohomology groups of line bundles. J. Am. Math. Soc. 4, 87–103
Hartshorne R. (1971) Ample vector bundles on curves. Nagoya Math. J. 43, 73–89
Hacon, C.D., McKernan, J.: Boundedness of pluricanonical maps of varieties of general type. Invent. Math. 2006 (in press)
Kollár J. (1986) Higher direct images of dualizing sheaves I. Ann. Math. 123, 11–42
Kollár J. (1986) Higher direct images of dualizing sheaves II. Ann. Math. 124, 171–202
Kollár, J.: Shafarevich maps and automorphic forms. In: M. B. Porter Lectures, Princeton University Press, Princeton 1995
Mukai S.(1981) Duality between D(X) and \(D(\hat {X})\) with its application to Picard sheaves. Nagoya Math. J. 81, 153–175
Takayama, S.: Pluricanonical systems on algebraic varieties of general type. Invent. Math (2006) (in press)
Todorov, G.: Pluricanonical maps for threefolds. Preprint math.AG/0512346
Tu L.W. (1993) Semistable Bundles over an elliptic curve. Adv. Math. 98, 1–26
Tsuji, H.: Pluricanonical systems of projective varieties of general type II. math.CV/0409318
Tsuji, H.: Pluricanonical systems of projective 3-folds of general type. math.AG/0204096
Viehweg E. (1983) Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces. Adv. Stud. Pure Math., North Holland, 1, 329–353
Viehweg, E.: Quasi-projective moduli for Polarized Manifolds. Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete 30 (1995)
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The first author was partially supported by NSC and NCTS of Taiwan. The second author was partially supported by NSF research grant no: 0456363.
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Chen, J.A., Hacon, C.D. Pluricanonical systems on irregular 3-folds of general type. Math. Z. 255, 343–355 (2007). https://doi.org/10.1007/s00209-006-0028-9
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DOI: https://doi.org/10.1007/s00209-006-0028-9