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**11 - 18**of**18**### 2 A UNIQUENESS THEOREM FOR FROBENIUS MANIFOLDS AND GROMOV–WITTEN THEORY FOR ORBIFOLD PROJECTIVE LINES

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"... Abstract. We compute quantum cohomology rings of elliptic P1 orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of orbi-curves are related to the integer solutions of Diophantine equ ..."

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Abstract. We compute quantum cohomology rings of elliptic P1 orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of orbi-curves are related to the integer solutions of Diophantine equations. This reproduces the computation of Satake and Taka-hashi in the case of P13,3,3 via different method.

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"... cu ol a In ter naz ional e Superiore di Studi Avanzati- ma per seguir virtute e con osc enz a-PhD Thesis ..."

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cu ol a In ter naz ional e Superiore di Studi Avanzati- ma per seguir virtute e con osc enz a-PhD Thesis