no. 15-16
Algebraic Geometry
Hodge structures and Weierstrass σ-function
[Structures de Hodge et fonction σ de Weierstrass]
Présenté par : Christophe Soulé
Banaszak, Grzegorz1 ; Milewski, Jan2
1 Department of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland
2 Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3A, 60-965 Poznań, Poland
Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 777-780

In this Note we introduce new definition of Hodge structures and show that R-Hodge structures are determined by R-linear operators that are annihilated by the Weierstrass σ-function.

Dans cette Note, nous introduisons une nouvelle définition des structures de Hodge et démontrons que les structures de Hodge sur R sont déterminées par des transformations R-linéaires qui sont des zéros de la fonction σ de Weierstrass.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.09.012

Banaszak, Grzegorz 1 ; Milewski, Jan 2

1 Department of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland
2 Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3A, 60-965 Poznań, Poland 
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Banaszak, Grzegorz; Milewski, Jan. Hodge structures and Weierstrass σ-function. Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 777-780. doi: 10.1016/j.crma.2012.09.012

[1] Banaszak, G.; Milewski, J. Hodge structures in topological quantum mechanics, J. Phys. Conf. Ser., Volume 213 (2010), p. 012017

[2] Gordon, B. A survey of the Hodge conjecture for abelian varieties (Lewis, J., ed.), A Survey of the Hodge Conjecture, American Mathematical Society, 1999, pp. 297-356 (Appendix B)

[3] Milewski, J. Holomorphons and the standard almost complex structure on S6, Comment. Math., Volume XLVI (2006) no. 2, pp. 245-254

[4] Milewski, J. Holomorphons on spheres, Comment. Math., Volume B XLVIII (2008) no. 2, pp. 13-22

[5] Peters, C.; Steenbrink, J. Mixed Hodge Structures, Ergeb. Math. Grenzgeb., vol. 52, Springer, 2008

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