Kawamata, Yujiro Characterization of abelian varieties. (English) Zbl 0471.14022 Compos. Math. 43, 253-276 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 11 ReviewsCited in 137 Documents MSC: 14K10 Algebraic moduli of abelian varieties, classification 14J15 Moduli, classification: analytic theory; relations with modular forms 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 14E05 Rational and birational maps Keywords:Albanese mapping; Kodaira dimension; variation of Hodge structures PDFBibTeX XMLCite \textit{Y. Kawamata}, Compos. Math. 43, 253--276 (1981; Zbl 0471.14022) Full Text: Numdam EuDML References: [1] P. Deligne : Theorie de Hodge II . Publ. Math. IHES, 40 (1971) 5-58. · Zbl 0219.14007 [2] T. Fujita : On Kaehler fiber spaces over curves . J. Math. Soc. Japan, 30 (1978) 779-794. · Zbl 0393.14006 [3] P. Griffiths : Periods of integrals on algebraic manifolds III . Publ. Math. IHES, 38 (1970) 125-180. · Zbl 0212.53503 [4] R. Hartshorne : Ample subvarieties of algebraic varieties . Lec. Note in Math. 156, Springer, 1970. · Zbl 0208.48901 [5] S. Iitaka : On D-dimensions of algebraic varieties . J. Math. Soc. Japan, 23 (1971), 356-373. · Zbl 0212.53802 [6] S. Iitaka : On logarithmic Kodaira dimension of algebraic varieties . Complex Analysis and Algebraic Geometry , 1977, Iwanami, Tokyo. · Zbl 0351.14016 [7] S. Iitaka : Logarithmic form of algebraic varieties . J. Fac. Sci. Univ. Tokyo, 23 (1976) 525-544. · Zbl 0342.14017 [8] Y. Kawamata : Addition formula of logarithmic Kodaira dimension for morphisms of relative dimension one . Proc. Alg. Geo. Kyoto, 1977 , Kinokuniya, Tokyo, 207-217. · Zbl 0437.14018 [9] Y. Kawamata and E. Viehweg : On a characterization of an abelian variety in the classification theory of algebraic varieties . Compositio Math., 41 (1980) 355-360. · Zbl 0417.14033 [10] K. Kodaira : Holomorphic mappings of polydiscs into compact complex manifolds . J. Diff. Geo., 6 (1971) 33-46. · Zbl 0227.32008 [11] F. Sakai : Kodaira dimensions of complements of divisors . Complex Analysis and Algebraic Geometry, 1977, Iwanami, 239-257. · Zbl 0375.14009 [12] W. Schmid : Variation of Hodge structure: the singularities of period mapping . Inv. Math., 22 (1973) 211-319. · Zbl 0278.14003 [13] K. Ueno : Classification theory of algebraic varieties and compact complex spaces . Lec. Note in Math. 439, Springer, 1975. · Zbl 0299.14007 [14] K. Ueno : On algebraic fiber spaces of abelian varieties . Math. Ann., 237 (1978) 1-22. · Zbl 0368.14013 [15] K. Ueno : Classification of algebraic varieties II . Proc. Alg. Geo. Kyoto, 1977 , Kinokuniya, Tokyo, 693-708. · Zbl 0407.14011 [16] E. Viehweg : Canonical divisors and the additivity of the Kodaira dimensions for morphisms of relative dimension one . Compositio Math., 35 (1977), 197-223. · Zbl 0357.14014 [17] E. Viehweg : Klassifikationstheorie algebraischer Varietaeten der Dimension drei . Compositio Math., 41 (1980) 361-400. · Zbl 0414.14017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.