Translator Disclaimer
2001 Recovery of vanishing cycles by log geometry
Sampei Usui
Tohoku Math. J. (2) 53(1): 1-36 (2001). DOI: 10.2748/tmj/1178207529


We first construct compatible actions of the product of the unit interval and the unit circle as a monoid on a semi-stable degeneration of pairs and on the associated log topological spaces. Then we show that the log topological family is locally trivial in piecewise smooth category over the base, i.e., the associated log topological family recovers the vanishing cycles of the original semi-stable degeneration in the most naive sense. Using this result together with the log Riemann-Hilbert correspondence, we introduce two types of integral structure of the variation of mixed Hodge structure associated to a semi-stable degeneration of pairs.


Download Citation

Sampei Usui. "Recovery of vanishing cycles by log geometry." Tohoku Math. J. (2) 53 (1) 1 - 36, 2001.


Published: 2001
First available in Project Euclid: 3 May 2007

zbMATH: 1015.14005
MathSciNet: MR1808639
Digital Object Identifier: 10.2748/tmj/1178207529

Primary: 32G20
Secondary: 14C25, 14D07, 32J25

Rights: Copyright © 2001 Tohoku University


Vol.53 • No. 1 • 2001
Back to Top