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.

Received:
Accepted:
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
@article{CRMATH_2012__350_15-16_777_0,
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2012.09.012/}
}
TY  - JOUR
AU  - Banaszak, Grzegorz
AU  - Milewski, Jan
TI  - Hodge structures and Weierstrass σ-function
JO  - Comptes Rendus. Mathématique
PY  - 2012
SP  - 777
EP  - 780
VL  - 350
IS  - 15-16
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2012.09.012/
DO  - 10.1016/j.crma.2012.09.012
LA  - en
ID  - CRMATH_2012__350_15-16_777_0
ER  - 
%0 Journal Article
%A Banaszak, Grzegorz
%A Milewski, Jan
%T Hodge structures and Weierstrass σ-function
%J Comptes Rendus. Mathématique
%D 2012
%P 777-780
%V 350
%N 15-16
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2012.09.012/
%R 10.1016/j.crma.2012.09.012
%G en
%F CRMATH_2012__350_15-16_777_0
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. http://www.numdam.org/articles/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

Cited by Sources: