Using discriminant curves to recover a surface of P4 from two generic linear projections

Jeremy Yrmeyahu Kaminski; Yann Sepulcre

doi:10.1145/1993886.1993917

Using discriminant curves to recover a surface of P⁴ from two generic linear projections

Jeremy Yrmeyahu Kaminski, Yann Sepulcre

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We study how an irreducible smooth and closed algebraic surface X embedded in CP⁴, 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 CP⁴ can be recovered modulo some action of the group of projective transformations of CP⁴. 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
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	https://doi.org/10.1145/1993886.1993917
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

Conference

Conference	36th International Symposium on Symbolic and Algebraic Computation, ISSAC 2011
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

Access to Document

10.1145/1993886.1993917

Cite this

Kaminski, J. Y., & Sepulcre, Y. (2011). Using discriminant curves to recover a surface of P⁴ from two generic linear projections. In ISSAC 2011 - Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (pp. 187-192). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1993886.1993917

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abstract = "We study how an irreducible smooth and closed algebraic surface X embedded in CP4, 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 CP4 can be recovered modulo some action of the group of projective transformations of CP4. 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.",

keywords = "algebraic surfaces, computational algebraic geometry, discriminant curves, linear projections",

author = "Kaminski, {Jeremy Yrmeyahu} and Yann Sepulcre",

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Kaminski, JY & Sepulcre, Y 2011, Using discriminant curves to recover a surface of P⁴ from two generic linear projections. in ISSAC 2011 - Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 187-192, 36th International Symposium on Symbolic and Algebraic Computation, ISSAC 2011, San Jose, CA, United States, 8/06/11. https://doi.org/10.1145/1993886.1993917

Using discriminant curves to recover a surface of P⁴ from two generic linear projections. / Kaminski, Jeremy Yrmeyahu; Sepulcre, Yann.
ISSAC 2011 - Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation. 2011. p. 187-192 (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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