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The ${}^{12}\mathrm{C} + {}^{12}\mathrm{C}$ fusion reaction plays a vitalrole in the explosive phenomena of the universe. The resonances in the Gamowwindow rule its reaction rate and products. Hence, the determination of theresonance parameters by nuclear models is indispensable as the directmeasurement is not feasible. Here, for the first time, we report the resonancesin the ${}^{12}\mathrm{C} + {}^{12}\mathrm{C}$ fusion reaction described by afull-microscopic nuclear model. The model plausibly reproduces the measuredlow-energy astrophysical $S$-factors and predicts the resonances in the Gamowwindow. Contradictory to the hindrance model, we conclude that there is nolow-energy suppression of the $S$-factor.

$\mathbf{{}^{12}{C} + {}^{12}{C}}$ Fusion $\boldsymbol{S^*}$-factor from a Full-microscopic Nuclear Model