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We propose matter wavefunctions on resolutions of $T^2/\mathbb{Z}_N$singularities with constant magnetic fluxes. In the blow-down limit, theobtained wavefunctions of chiral zero-modes result in those on the magnetized$T^2/\mathbb{Z}_N$ orbifold models, but the wavefunctions of$\mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixedpoints of $T^2/\mathbb{Z}_N$ orbifolds. Such blow-up effects change theselection rules and Yukawa couplings among the chiral zero-modes as well as themodular symmetry, in contrast to those on the magnetized $T^2/\mathbb{Z}_N$orbifold models.

Wavefunctions and Yukawa Couplings on Resolutions of $T^2/\mathbb{Z}_N$ Orbifolds