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In this paper study the quantum deformation of the superflag Fl(2|0,2|1,4|1), and its big cell, describing the complex conformal and Minkowskisuperspaces respectively. In particular, we realize their projective embeddingvia a generalization to the super world of the Segre map and we use it toconstruct a quantum deformation of the super line bundle realizing thisembedding. This strategy allows us to obtain a description of the quantumcoordinate superring of the superflag that is then naturally equipped with acoaction of the quantum complex conformal supergroup SL_q(4|1).

The Segre embedding of the quantum conformal superspace