## Kodai Mathematical Journal

### Degeneration of period matrices of stable curves

Yu Yang

#### Abstract

In the present paper, we study the extent to which linear combinations of period matrices arising from stable curves are degenerate (i.e., as bilinear forms). We give a criterion to determine whether a stable curve admits such a degenerate linear combination of period matrices. In particular, this criterion can be interpreted as a certain analogue of the weight-monodromy conjecture for non-degenerate elements of pro-$\ell$ log étale fundamental groups of certain log points associated to the log stack $\overline{\mathcal{M}}_{g}^{log}$.

#### Article information

Source
Kodai Math. J., Volume 41, Number 1 (2018), 125-153.

Dates
First available in Project Euclid: 19 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1521424828

Digital Object Identifier
doi:10.2996/kmj/1521424828

Mathematical Reviews number (MathSciNet)
MR3777391

Zentralblatt MATH identifier
06912405

#### Citation

Yang, Yu. Degeneration of period matrices of stable curves. Kodai Math. J. 41 (2018), no. 1, 125--153. doi:10.2996/kmj/1521424828. https://projecteuclid.org/euclid.kmj/1521424828