Tau function and moduli of differentials
Algebraic Geometry
2011-06-03 v2 Mathematical Physics
Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves. The asymptotics of the tau function near the boundary of the moduli space of 1-differentials is computed, and an explicit expression for the pullback of the Hodge class on the projectivized Hodge bundle in terms of the tautological class and the classes of boundary divisors is derived. This expression is used to clarify the geometric meaning of the Kontsevich-Zorich formula for the sum of the Lyapunov exponents associated with the Teichm\"uller flow on the Hodge bundle.
Cite
@article{arxiv.1003.2173,
title = {Tau function and moduli of differentials},
author = {Dmitry Korotkin and Peter Zograf},
journal= {arXiv preprint arXiv:1003.2173},
year = {2011}
}
Comments
misprints corrected; journal reference added