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We construct a smooth algebraic stack of tuples consisting of genus two nodalcurves, line bundles, and twisted fields. It leads to a desingularization ofthe moduli of genus two stable maps to projective spaces. The construction isbased on systematical application of the theory of stacks with twisted fields(STF), which has its prototype appeared in arXiv:1906.10527 and arXiv:1201.2427and is fully developed in this article. The results of this article are thesecond step of a series of works toward the resolutions of the moduli of stablemaps of higher genera.

A theory of stacks with twisted fields and resolution of moduli of genus two stable maps