Mixed Hodge structures on Alexander modules
"Motivated by the limit mixed Hodge structure on the Milnor fiber of a hypersurface singularity germ, we construct a natural mixed Hodge structure on the torsion part of the Alexander modules of a smooth connected complex algebraic variety. More precisely, let U be a smooth connected complex al...
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Tag hinzufügen | Zusammenfassung: | "Motivated by the limit mixed Hodge structure on the Milnor fiber of a hypersurface singularity germ, we construct a natural mixed Hodge structure on the torsion part of the Alexander modules of a smooth connected complex algebraic variety. More precisely, let U be a smooth connected complex algebraic variety and let f : U C be an algebraic map inducing an epimorphism in fundamental groups. The pullback of the universal cover of C by f gives rise to an infinite cyclic cover Uf of U. The action of the deck group Z on Uf induces a Q[t1]- module structure on H(Uf ;Q). We show that the torsion parts A(Uf ;Q) of the Alexander modules H(Uf ;Q) carry canonical Q-mixed Hodge structures. We also prove that the covering map Uf U induces a mixed Hodge structure morphism on the torsion parts of the Alexander modules. As applications, we investigate the semisimplicity of A(Uf ;Q), as well as possible weights of the constructed mixed Hodge structures. Finally, in the case when f : U C is proper, we prove the semisimplicity and purity of A(Uf ;Q), and we compare our mixed Hodge structure on A(Uf ;Q) with the limit mixed Hodge structure on the generic fiber of f"-- |
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| Beschreibung: | "April 2024, volume 296, number 1479 (fifth of 7 numbers)" Literaturverzeichnis: Seite 109-111 Description based on publisher supplied metadata and other sources |
| Beschreibung: | viii, 114 Seiten |
| ISBN: | 9781470469672 978-1-4704-6967-2 |