Abstract. Let X be an n-dimensional normal projective variety with terminal, Gorenstein, Qfactorial singularities. Let L be an ample line bundle on X . Let t be the nefvalue of ðX ; LÞ. Then we classify ðX ; LÞ, describing the structure of the nefvalue morphism of ðX ; LÞ, when t satisfies n À k < t < n À k þ 1 and n d 2k À 3, k d 4. In the smooth case, we discuss the case n ¼ 2k À 4, k d 5, as well. Key words. Complex polarized n-fold, ample line bundle, nefvalue, nefvalue morphism, Gorenstein, terminal, Q-factorial singularities, adjunction theory, special varieties. 2000 Mathematics Subject Classification. Primary 14N30, 14J40; Secondary 14J45, 14C20 Introduction Let X be an n-dimensional projective variety with terminal, Gorenstein, Q-factorial singularities and let L be an ample line bundle on X . If the canonical bundle KX is not nef, the Kawamata rationality theorem and the KawamataShokurov basepoint free theorem imply that there is a fraction t ¼ u=v, with u, v positive coprime integers, and a morphism f : X ! W with connected fibers onto a normal projective variety W such that vKX þ
Advances in Geometry – de Gruyter
Published: Aug 19, 2003
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