Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00209-007-0186-4
Title: Characterization of the 4-canonical birationality of algebraic threefolds
Authors: Chen, M.
Zhang, D.-Q. 
Issue Date: Mar-2008
Citation: Chen, M., Zhang, D.-Q. (2008-03). Characterization of the 4-canonical birationality of algebraic threefolds. Mathematische Zeitschrift 258 (3) : 565-585. ScholarBank@NUS Repository. https://doi.org/10.1007/s00209-007-0186-4
Abstract: In this article we present a 3-dimensional analogue of a well-known theorem of Bombieri (Inst Hautes Etudes Sci Publ Math 42:171-219, 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let X be a projective minimal threefold of general type with ℚ-factorial terminal singularities and the geometric genus p g X 5. We show that the 4-canonical map 4 is not birational onto its image if and only if X is birationally fibred by a family C of irreducible curves of geometric genus 2 with KXC 0 =1 where C 0 is a general irreducible member in C. © 2007 Springer-Verlag.
Source Title: Mathematische Zeitschrift
URI: http://scholarbank.nus.edu.sg/handle/10635/102979
ISSN: 00255874
DOI: 10.1007/s00209-007-0186-4
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