## Abstract

We 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. We 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}. We show how in a generic situation, a characteristic matrix of the pair of embeddings can be recovered. Then we 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.

Original language | English |
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Title of host publication | ISSAC 2011 - Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation |

Pages | 187-192 |

Number of pages | 6 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | 36th International Symposium on Symbolic and Algebraic Computation, ISSAC 2011 - San Jose, CA, United States Duration: 8 Jun 2011 → 11 Jun 2011 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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### Conference

Conference | 36th International Symposium on Symbolic and Algebraic Computation, ISSAC 2011 |
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Country/Territory | United States |

City | San Jose, CA |

Period | 8/06/11 → 11/06/11 |

## Keywords

- algebraic surfaces
- computational algebraic geometry
- discriminant curves
- linear projections

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