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In this paper we prove rigidity for blowup solutions to the focusing,mass-critical nonlinear Schr{\"o}dinger equation in dimensions $2 \leq d \leq15$ with mass equal to the mass of the soliton. We prove that the only suchsolutions are the solitons and the pseudoconformal transformation of thesolitons.

A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton