Mixed Hodge structures and Weierstrass <i>σ</i>-function

Banaszak, Grzegorz; Milewski, Jan

doi:10.1016/j.crma.2013.07.015

Algebraic Geometry

Mixed Hodge structures and Weierstrass σ-function
[Structures de Hodge mixtes et fonction σ de Weierstrass]

Présenté par : the Editorial Board

Banaszak, Grzegorz ¹ ; Milewski, Jan ²

¹ Department of Mathematics and Computer Science, Adam Mickiewicz University, Poznań 61-614, Poland
² Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3A, 60-965 Poznań, Poland

Comptes Rendus. Mathématique, Tome 351 (2013) no. 13-14, pp. 551-555.

Résumé
Abstract

Un σ-opérateur sur la complexification $V_{C}$ dʼun espace vectoriel réel $V_{R}$ est un opérateur $A \in {End}_{C} (V_{C})$ tel que $σ (A) = 0$ , où $σ (z)$ est la fonction σ de Weierstrass. Dans cet article, nous introduisons la notion de σ-opérateur fortement pseudo-réel et démontrons quʼil y a une correspondance biunivoque entre les structures de Hodge mixtes réelles et les σ-opérateurs fortement pseudo-réels.

A σ-operator on a complexification $V_{C}$ of an $R$ -vector space $V_{R}$ is an operator $A \in {End}_{C} (V_{C})$ such that $σ (A) = 0$ , where $σ (z)$ denotes the Weierstrass σ-function. In this paper, we define the notion of strongly pseudo-real σ-operator and prove that there is a one-to-one correspondence between real mixed Hodge structures and strongly pseudo-real σ-operators.

Reçu le : 2012-11-03
Accepté le : 2013-07-18
Publié le : 2013-07-01

DOI : 10.1016/j.crma.2013.07.015

Affiliations des auteurs :

Banaszak, Grzegorz ¹ ; Milewski, Jan ²

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Banaszak, Grzegorz; Milewski, Jan. Mixed Hodge structures and Weierstrass σ-function. Comptes Rendus. Mathématique, Tome 351 (2013) no. 13-14, pp. 551-555. doi : 10.1016/j.crma.2013.07.015. http://www.numdam.org/articles/10.1016/j.crma.2013.07.015/

Bibliographie
Cité par

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[4] Deligne, P. Structures de Hodge mixtes réelles, Proc. Symp. Pure Math., Volume 55 (1994), pp. 509-514

[5] Gordon, B. A survey of the Hodge conjecture for Abelian varieties (Lewis, J., ed.), A Survey of the Hodge Conjecture, 1999, pp. 297-356 (Appendix B)

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

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