A description of a result of Deligne by log higher Albanese map

Sampei Usui

Journal of Singularities
volume 21 (2020), 282-300

Received: 23 March 2018. Received in revised form: 17 September 2018.

DOI: 10.5427/jsing.2020.21q

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Abstract:

In a joint work with Kazuya Kato and Chikara Nakayama, log higher Albanese manifolds were constructed as an application of log mixed Hodge theory with group action. In this framework, we describe a work of Deligne on some nilpotent quotients of the fundamental group of the projective line minus three points, where polylogarithms appear. As a result, we have q-expansions of higher Albanese maps at boundary points, i.e., log higher Albanese maps over the boundary.

2010 Mathematical Subject Classification:

Primary 14C30; Secondary 14D07, 32G20

Key words and phrases:

Hodge theory, log Hodge structure, log higher Albanese map, polylogarithm, zeta value

Author(s) information:

Sampei Usui
Graduate School of Science
Osaka University
Toyonaka, Osaka, 560-0043, Japan
email: usui@math.sci.osaka-u.ac.jp