Translator Disclaimer
March 2020 Local comparisons of homological and homotopical mixed Hodge polynomials
Shoji Yokura
Proc. Japan Acad. Ser. A Math. Sci. 96(3): 28-31 (March 2020). DOI: 10.3792/pjaa.96.006

Abstract

For a simply connected complex algebraic variety $X$, by the mixed Hodge structures $(W_{\bullet}, F^{\bullet})$ and $(\tilde{W}_{\bullet}, \tilde{F}^{\bullet})$ of the homology group $H_{*}(X;\mathbf{Q})$ and the homotopy groups $\pi_{*}(X)\otimes \mathbf{Q}$ respectively, we have the following mixed Hodge polynomials \begin{equation*} \mathit{MH}_{X}(t,u,v):= ∑_{k,p,q} \dim (\mathit{Gr}_{F_{•}}^{p} \mathit{Gr}^{W_{•}}_{p+q} H_{k} (X;\mathbf{C})) t^{k} u^{-p} v^{-q}, \end{equation*} \begin{equation*} \mathit{MH}^{π}_{X}(t,u,v):= ∑_{k,p,q} \dim (\mathit{Gr}_{\tilde{F}_{•}}^{p} \mathit{Gr}^{\tilde{W}_{•}}_{p+q} (π_{k}(X) øtimes \mathbf{C})) t^{k}u^{-p} v^{-q}, \end{equation*} which are respectively called the homological mixed Hodge polynomial and the homotopical mixed Hodge polynomial. In this paper we discuss some inequalities concerning these two mixed Hodge polynomials.

Citation

Download Citation

Shoji Yokura. "Local comparisons of homological and homotopical mixed Hodge polynomials." Proc. Japan Acad. Ser. A Math. Sci. 96 (3) 28 - 31, March 2020. https://doi.org/10.3792/pjaa.96.006

Information

Published: March 2020
First available in Project Euclid: 3 March 2020

zbMATH: 07192785
MathSciNet: MR4071352
Digital Object Identifier: 10.3792/pjaa.96.006

Subjects:
Primary: 32S35, 55N99, 55P62, 55Q40

Rights: Copyright © 2020 The Japan Academy

JOURNAL ARTICLE
4 PAGES


SHARE
Vol.96 • No. 3 • March 2020
Back to Top