Comptes Rendus
no. 11-12
Algebraic Geometry/Number Theory
The locus of Hodge classes in an admissible variation of mixed Hodge structure

Presented by: Pierre Deligne

Patrick Brosnan1; Gregory Pearlstein2; Christian Schnell3
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

Patrick Brosnan 1; Gregory Pearlstein 2; Christian Schnell 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 
@article{CRMATH_2010__348_11-12_657_0,
     author = {Patrick Brosnan and Gregory Pearlstein and Christian Schnell},
     title = {The locus of {Hodge} classes in an admissible variation of mixed {Hodge} structure},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {657--660},
     publisher = {Elsevier},
     volume = {348},
     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.002},
     language = {en},
}
TY  - JOUR
AU  - Patrick Brosnan
AU  - Gregory Pearlstein
AU  - Christian Schnell
TI  - The locus of Hodge classes in an admissible variation of mixed Hodge structure
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 657
EP  - 660
VL  - 348
IS  - 11-12
PB  - Elsevier
DO  - 10.1016/j.crma.2010.04.002
LA  - en
ID  - CRMATH_2010__348_11-12_657_0
ER  - 
%0 Journal Article
%A Patrick Brosnan
%A Gregory Pearlstein
%A Christian Schnell
%T The locus of Hodge classes in an admissible variation of mixed Hodge structure
%J Comptes Rendus. Mathématique
%D 2010
%P 657-660
%V 348
%N 11-12
%I Elsevier
%R 10.1016/j.crma.2010.04.002
%G en
%F CRMATH_2010__348_11-12_657_0
Patrick Brosnan; Gregory Pearlstein; Christian Schnell. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.002/

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

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

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

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

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

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

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

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

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

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

Cited by Sources:

Comments - Policy