@article{Wang2026, 
author = {Zhiyuan Wang and Jian Zhou},
title = {Orbifold Euler Characteristics of                                                          M                                      ¯                    g      ,      n},
year = {2026},
journal = {Peking Mathematical Journal},
volume = {9},
number = {3},
pages = {577-628},
keywords = {Moduli spaces of stable curves, Orbifold Euler characteristics, Recursions, KP hierarchy},
url = {https://www.sciopen.com/article/10.1007/s42543-025-00110-5},
doi = {10.1007/s42543-025-00110-5},
abstract = {We compute the orbifold Euler characteristics of                      M            ¯              g      ,      n       by applying the formalisms developed in (Wang et al., J. High Energy Phys. 2019(4):135, 2019; Zhou, arXiv:1412.1604, 2014).We take the works of Harer–Zagier (Invent. Math. 85(3):457–485, 1986) and Bini–Harer (J. Eur. Math. Soc. 13(2):487–512, 2011) as the starting point, and prove two types of recursion relations to compute    χ  (                              M                    ¯              g      ,      n        ). As applications of these recursions, we give some numerical data and derive some closed formulas, and generalize Manin’s functional equation for    χ  (                              M                    ¯              0      ,      n        ) to higher genera cases. Moreover, in genus zero the results are related to Ramanujan polynomials. We also show that the generating series of    χ  (                                                        M                                      ¯                    g      ,      n        ) is the logarithm of a particular tau-function of KP hierarchy evaluated at times specified by the generating series of    χ  (                              M                            g      ,      n        ).}
}