Algebraic Geometry/Number Theory
The locus of Hodge classes in an admissible variation of mixed Hodge structure

Presented by: Pierre Deligne

Brosnan, Patrick1; Pearlstein, Gregory2; Schnell, Christian3
1 Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
3 Department of Mathematics, Statistics & Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA
Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 657-660.

We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.

On généralise le théorème de E. Cattani, P. Deligne, et A. Kaplan aux variations de structure de Hodge mixtes admissibles.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.04.002
Brosnan, Patrick 1; Pearlstein, Gregory 2; Schnell, Christian 3

1 Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., Canada V6T 1Z2
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
3 Department of Mathematics, Statistics & Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA 
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Brosnan, Patrick; Pearlstein, Gregory; Schnell, Christian. The locus of Hodge classes in an admissible variation of mixed Hodge structure. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 657-660. doi : 10.1016/j.crma.2010.04.002. http://archive.numdam.org/articles/10.1016/j.crma.2010.04.002/

[1] Brosnan, P.; Pearlstein, G. On the algebraicity of the zero locus of an admissible normal function, 2009 | arXiv

[2] Cattani, E.; Deligne, P.; Kaplan, A. On the locus of Hodge classes, J. Amer. Math. Soc., Volume 8 (1995) no. 2, pp. 483-506

[3] Hironaka, H. Bimeromorphic smoothing of a complex-analytic space, Acta Math. Vietnam., Volume 2 (1977) no. 2, pp. 103-168

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

[5] Kato, K.; Nakayama, C.; Usui, S. SL(2)-orbit theorem for degeneration of mixed Hodge structure, J. Algebraic Geom., Volume 17 (2008) no. 3, pp. 401-479

[6] Kato, K.; Nakayama, C.; Usui, S. Moduli of log mixed Hodge structures, 2009 http://arXiv.org/abs/0910.4454

[7] Saito, M. Admissible normal functions, J. Algebraic Geom., Volume 5 (1996) no. 2, pp. 235-276

[8] Saito, M. Arithmetic mixed sheaves, Invent. Math., Volume 144 (2001) no. 3, pp. 533-569

[9] Schnell, C. Complex-analytic Neron models for arbitrary families of intermediate Jacobians, 2009 http://arXiv.org/abs/0910.0662

[10] Steenbrink, J.; Zucker, S. Variation of mixed Hodge structure. I, Invent. Math., Volume 80 (1985) no. 3, pp. 489-542

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