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Comptes Rendus Mathématique
Volume 351, n° 13-14
pages 551-555 (juillet 2013)
Doi : 10.1016/j.crma.2013.07.015
Received : 3 November 2012 ;  accepted : 18 July 2013
Mixed Hodge structures and Weierstrass σ -function
Structures de Hodge mixtes et fonction σ de Weierstrass
 

Grzegorz Banaszak a, 1 , Jan Milewski b
a Department of Mathematics and Computer Science, Adam Mickiewicz University, Poznań 61-614, Poland 
b Institute of Mathematics, Poznań University of Technology, ul. Piotrowo 3A, 60-965 Poznań, Poland 

Abstract

A σ -operator on a complexification   of an  -vector space   is an operator   such that  , where   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.

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Résumé

Un σ -opérateur sur la complexification   dʼun espace vectoriel réel   est un opérateur   tel que  , où   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.

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1  Partially supported by the NCN (National Center of Science for Poland) NN201 607440.


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