Moduli of log mixed Hodge structures

Moduli of log mixed Hodge structures

Kazuya Kato, Chikara Nakayama, and Sampei Usui

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 7 (2010), 107-112.

Abstract

We announce the construction of toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized graded quotients. We include an application to the analyticity of zero loci of normal functions.

First Page: Show

Primary Subjects: 14C30

Secondary Subjects: 14D07, 32G20

Keywords: Hodge theory; log geometry; Griffiths domain; toroidal compactification; log mixed Hodge structure; admissible normal function

Full-text: Open access

PDF File (125 KB)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1279719310
Digital Object Identifier: doi:10.3792/pjaa.86.107
Mathematical Reviews number (MathSciNet): MR2657330
Zentralblatt MATH identifier: 05835892

back to Table of Contents

References

A. Borel, Introduction aux groupes arithmétiques, Hermann, Paris, 1969.

Mathematical Reviews (MathSciNet): MR244260

P. Brosnan and G. J. Pearlstein, Zero loci of admissible normal functions with torsion singularities, arXiv:0803.3365.

P. Brosnan and G. J. Pearlstein, On the algebraicity of the zero locus of an admissible normal function, arXiv:0910.0628.

Mathematical Reviews (MathSciNet): MR2552111

Zentralblatt MATH: 1184.32004

Digital Object Identifier: doi:10.4007/annals.2009.170.883

E. Cattani, A. Kaplan and W. Schmid, Degeneration of Hodge structures, Ann. of Math. (2) 123 (1986), no. 3, 457--535.

Mathematical Reviews (MathSciNet): MR840721

Digital Object Identifier: doi:10.2307/1971333

JSTOR: links.jstor.org

P. Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. No. 52 (1980), 137--252.

Mathematical Reviews (MathSciNet): MR601520

Digital Object Identifier: doi:10.1007/BF02684780

P. A. Griffiths, Periods of integrals on algebraic manifolds, I. Construction and properties of the modular varieties, Amer. J. Math. 90 (1968), 568--626.

Mathematical Reviews (MathSciNet): MR229641

Zentralblatt MATH: 0169.52303

Digital Object Identifier: doi:10.2307/2373545

JSTOR: links.jstor.org

M. Kashiwara, A study of variation of mixed Hodge structure, Publ. Res. Inst. Math. Sci. 22 (1986), no. 5, 991--1024.

Mathematical Reviews (MathSciNet): MR866665

Digital Object Identifier: doi:10.2977/prims/1195177264

K. Kato, Logarithmic structures of Fontaine-Illusie, in Algebraic analysis, geometry, and number theory (J.-I. Igusa, ed.), (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, (1989), 191--224.

Mathematical Reviews (MathSciNet): MR1463703

Zentralblatt MATH: 0776.14004

K. Kato and C. Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over $\mathbfC$, Kodai Math. J. 22 (1999), no. 2, 161--186.

Mathematical Reviews (MathSciNet): MR1700591

Digital Object Identifier: doi:10.2996/kmj/1138044041

Project Euclid: euclid.kmj/1138044041

K. Kato, C. Nakayama and S. Usui, $\mathop\mathrmSL(2)$-orbit theorem for degeneration of mixed Hodge structure, J. Algebraic Geom. 17 (2008), no. 3, 401--479.

Mathematical Reviews (MathSciNet): MR2395135

Zentralblatt MATH: 1144.14005

K. Kato, C. Nakayama and S. Usui, Log intermediate Jacobians, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), 73--78.

K. Kato, C. Nakayama and S. Usui, Classifying spaces of degenerating mixed Hodge structures, II: Spaces of $\mathop\mathrmSL(2)$-orbits. (Preprint).

K. Kato, C. Nakayama and S. Usui, Classifying spaces of degenerating mixed Hodge structures, III: Spaces of nilpotent orbits. (in preparation).

K. Kato and S. Usui, Classifying spaces of degenerating polarized Hodge structures, Ann. of Math. Stud., 169, Princeton Univ. Press, Princeton, NJ, 2009.

Mathematical Reviews (MathSciNet): MR2465224

Zentralblatt MATH: 1172.14002

M. Saito, Hausdorff property of the Néron models of Green, Griffiths and Kerr, arXiv:0803.2771.

C. Schnell, Complex analytic Néron models for arbitrary families of intermediate Jacobians, arXiv:0910.0662.

J. H. M. Steenbrink and S. Zucker, Variation of mixed Hodge structure. I, Invent. Math. 80 (1985), no. 3, 489--542.

Mathematical Reviews (MathSciNet): MR791673

Zentralblatt MATH: 0626.14007

Digital Object Identifier: doi:10.1007/BF01388729

S. Usui, Variation of mixed Hodge structure arising from family of logarithmic deformations II: Classifying space, Duke Math. J. 51 (1984), no. 4, 851--875.

Mathematical Reviews (MathSciNet): MR771384

Digital Object Identifier: doi:10.1215/S0012-7094-84-05137-8

Project Euclid: euclid.dmj/1077304097

previous :: next