Algebraic Geometry
Hodge structures and Weierstrass σ-function
Comptes Rendus. Mathématique, Volume 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.

Published online:
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
     author = {Banaszak, Grzegorz and Milewski, Jan},
     title = {Hodge structures and {Weierstrass} \protect\emph{\ensuremath{\sigma}}-function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {777--780},
     publisher = {Elsevier},
     volume = {350},
     number = {15-16},
     year = {2012},
     doi = {10.1016/j.crma.2012.09.012},
     language = {en},
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Banaszak, Grzegorz; Milewski, Jan. Hodge structures and Weierstrass σ-function. Comptes Rendus. Mathématique, Volume 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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