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Analytic Log Picard Varieties

Published online by Cambridge University Press:  11 January 2016

Takeshi Kajiwara ,
Kazuya Kato  and
Chikara Nakayama
Takeshi Kajiwara
Affiliation:
Department of Applied mathematics, Faculty of Engineering, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, Japan, [email protected]
Kazuya Kato
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan, [email protected]
Chikara Nakayama
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152-8551, Japan, [email protected]
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Abstract

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We introduce a log Picard variety over the complex number field by the method of log geometry in the sense of Fontaine-Illusie, and study its basic properties, especially, its relationship with the group of log version of m-torsors.

Keywords

14K3014K2032G20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 191 , 2008 , pp. 149 - 180
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

[1] Breen, L., Extensions du groupe additif, Publ. Math., Inst. Hautes Étud. Sci., 48 (1977), 39–125.Google Scholar
[2] Fujisawa, T., Limits of Hodge structures in several variables, Compositio Math., 115 (1999), 129–183.Google Scholar
[3] Fujisawa, T. and Nakayama, C., Mixed Hodge structures on log deformations, Rendiconti del Seminario Matematico di Padova, 110 (2003), 221–268.Google Scholar
[4] Illusie, L., Complexe cotangent et déformations I, II, Lect. Notes Math. 239, 283, Berlin-Heidelberg-New York, Springer, 1972.Google Scholar
[5] Illusie, L., Kato, K., and Nakayama, C., Quasi-unipotent logarithmic Riemann-Hilbert correspondences, J. Math. Sci. Univ. Tokyo, 12 (2005), 1–66.Google Scholar
[6] Kajiwara, T., Logarithmic compactifications of the generalized Jacobian variety, J Fac. Sci. Univ. Tokyo Sect. IA, Math., 40 (1993), 473–502.Google Scholar
[7] Kajiwara, T., Log jacobian varieties, I: Local theory, in preparation.Google Scholar
[8] Kajiwara, T., Kato, K., and Nakayama, C., Logarithmic abelian varieties, Part I: Complex analytic theory, J. Math. Sci. Univ. Tokyo, 15 (2008), 69–193.Google Scholar
[9] Kajiwara, T., Kato, K., and Nakayama, C., Logarithmic abelian varieties, Part II. Algebraic theory, Nagoya Math. J., 189 (2008), 63–138.Google Scholar
[10] Kajiwara, T. and Nakayama, C., Higher direct images of local systems in log Betti cohomology, preprint, submitted.Google Scholar
[11] Kashiwara, M., A study of variation of mixed Hodge structure, Publ. Res. Inst. Math. Sci., Kyoto Univ., 22 (1986), 991–1024.Google Scholar
[12] Kato, K., Matsubara, T., and Nakayama, C., Log C∞-functions and degenerations of Hodge structures, Advanced Studies in Pure Mathematics 36, Algebraic Geometry 2000, Azumino (Usui, S., Green, M., Illusie, L., Kato, K., Looijenga, E., Mukai, S., and Saito, S., eds.), 2002, pp. 269–320.Google Scholar
[13] Kato, K. and Nakayama, C., Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over ℂ, Kodai Math. J., 22 (1999), 161–186.Google Scholar
[14] Kato, K. and Usui, S., Classifying spaces of degenerating polarized Hodge structures, to appear in Ann. of Math. Studies, Princeton Univ. Press.Google Scholar
[15] Kato, K., Nakayama, C., and Usui, S., SL(2)-orbit theorem for degeneration of mixed Hodge structure, J. Algebraic Geometry, 17 (2008), 401–479.Google Scholar
[16] Kawamata, Y., On algebraic fiber spaces, Contemporary trends in algebraic geometry and algebraic topology (Chern, Shiing-Shen, Fu, Lei, and Hain, Richard, eds.), Nankai Tracts in Mathematics, vol. 5, World Scientific Publishing, 2002, pp. 135–154.Google Scholar
[17] Kawamata, Y. and Namikawa, Y., Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties, Invent. Math., 118 (1994), 395–409.Google Scholar
[18] Kempf, G., Knudsen, F., Mumford, D., and Saint-Donat, B., Toroidal embeddings, I, Lect. Notes Math. 339, 1973.Google Scholar
[19] MacLane, S., Homologie des anneaux et des modules, C.B.R.M. Louvain (1956), 55–80.Google Scholar
[20] Namikawa, Y., Toroidal degeneration of abelian varieties, II, Math. Ann., 245 (1979), 117–150.Google Scholar
[21] Saito, M., Modules de Hodge polarisables, Publ. RIMS, Kyoto Univ., 24 (1988), 849–995.Google Scholar
[22] Steenbrink, J. H. M., Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures, Math. Ann., 301 (1995), 105–118.Google Scholar
[23] Steenbrink, J. H. M. and Zucker, S., Variation of mixed Hodge structure. I, Invent. Math., 80 (1985), 489–542.CrossRefGoogle Scholar
[24] Vidal, I., Monodromie locale et fonctions Zôeta des log schémas, Geometric aspects of Dwork Theory, volume II (Adolphson, A., Baldassarri, F., Berthelot, P., Katz, N., and Loeser, F., eds.), Walter de Gruyter, Berlin, New York, 2004, pp. 983–1039.Google Scholar