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Log intermediate Jacobians. (English) Zbl 1200.14024

The paper under review is devoted to the study of degenerations of intermediate Jacobians by means of log geometry, introduced by Fontaine and Illusie and developed in the papers: [K. Kato, Algebraic analysis, geometry, and number theory, Proc. JAMI Inaugur. Conf., Baltimore/MD (USA) 1988, 191–224 (1989; Zbl 0776.14004); L. Illusie, Barsotti symposium in algebraic geometry. Memorial meeting in honor of Iacopo Barsotti, in Abano Terme, Italy, June 24-27, 1991. San Diego, CA: Academic Press. Perspect. Math. 15, 183–203 (1994; Zbl 0832.14015) and K. Kato and C. Nakayama, Kodai Math. J. 22, No. 2, 161–186 (1999; Zbl 0957.14015)]. It turns out that a family of intermediate Jacobians over a punctured disc can be extended to a log intermediate Jacobian over a disc, which is a fiber product in the category of geometrical generalized analytic spaces with an fs logarithmic structure, as defined in [K. Kato and S. Usui, Classifying spaces of degenerating polarized Hodge structures, Annals of Mathematics Studies 169. (Princeton), NJ: Princeton University Press. (2009; Zbl 1172.14002)].

MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D07 Variation of Hodge structures (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations
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