Stable maps of genus zero to flag spaces (Q1282195)

In this article the author studies the moduli stack of stable maps from a genus zero curve to generalized flag spaces \(W=G/P\). The spaces of geometric points of these stacks are not smooth but only orbifolds in general. Via calculation of a generating function their virtual Poincaré polynomials are obtained. The generating function satisfies a certain universal differential equation. The dependence on \(W\) is only due to the initial condition which involves the Eisenstein series of \(W=G/P\). The article is a sequel of an article by the same author [\textit{Yu. I. Manin}, The moduli space of curves, Proc. Conf., Texel Island 1994, Prog. Math. 129, 401-417 (1995; Zbl 0871.14022)], which deals with the moduli space \(\overline{M}_{0,n}\) of stable \(n\)-pointed curves of genus zero. It is remarkable that, up to a change of variable, the same differential equation appears. Some of the appearing formulas have to be corrected. This is done by the author [\textit{Yu. I. Manin}, Topol. Methods Nonlinear Anal. 15, No. 2, 401 (2000)]. The general results are not altered.