Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study how an irreducible smooth and closed algebraic surface  X  embedded in CP 4 , can be recovered using its projections from two points onto embedded projective hyperplanes. The different embeddings are unknown. The only input is the defining equation of each projected surface.  show how both the embeddings and the surface in CP 4  can be recovered modulo some action of the group of projective transformations of CP 4 .    show how in a generic situation, a characteristic matrix of the pair of embeddings can be recovered. Then  use this matrix to recover the class of the couple of maps and as a consequence to recover the surface.   For a generic situation, two projections define a surface with two irreducible components. One component has degree  d ( d -1) and the other has degree  d , being the original surface.
['Jeremy Yrmeyahu Kaminski', 'Yann Sepulcre']
I am writing a research paper on a idea Using discriminant curves to recover a surface of P 4 from two generic linear projections
[{"from": "human", "value": "I am writing a research paper on a idea Using discriminant curves to recover a surface of P 4 from two generic linear projections"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study how an irreducible smooth and closed algebraic surface  X  embedded in CP 4 , can be recovered using its projections from two points onto embedded projective hyperplanes. The different embeddings are unknown. The only input is the defining equation of each projected surface.  show how both the embeddings and the surface in CP 4  can be recovered modulo some action of the group of projective transformations of CP 4 .    show how in a generic situation, a characteristic matrix of the pair of embeddings can be recovered. Then  use this matrix to recover the class of the couple of maps and as a consequence to recover the surface.   For a generic situation, two projections define a surface with two irreducible components. One component has degree  d ( d -1) and the other has degree  d , being the original surface."}]