A purity theorem for configuration spaces of smooth compact algebraic varieties

Autor:	Gorinov, A. G.
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Geometry Mathematics - Algebraic Topology
Druh dokumentu:	Working Paper
Popis:	B. Totaro showed \cite{totaro} that the rational cohomology of configuration spaces of smooth complex projective varieties is isomorphic as an algebra to the $E_2$ term of the Leray spectral sequence corresponding to the open embedding of the configuration space into the Cartesian power. In this note we show that the isomorphism can be chosen to be compatible with the mixed Hodge structures. In particular, we prove that the mixed Hodge structures on the configuration spaces of smooth complex projective varieties are direct sums of pure Hodge structures. Comment: This paper has been withdrawn as R. Hain and E. Looijenga have found counter-examples to the main theorem
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1702.08428 Zobrazit plný text záznamu View this record from Arxiv