On certain families of elliptic curves in projective space

2002/05/17 by Igor Dolgachev, Igor V. Dolgachev, Dolgachev, Igor V.
Computer Science · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Historical and Political Studies #math.AG

paper · pdf · doi:10.48550/arxiv.math/0205197

15 pages, 1 figure

openalex publication_date 2002/05/17 · arxiv created 2002/06/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study families of elliptic curves of degree n+1 in Pⁿ containing a fixed set of m points. In the case m = n+3 we show that this family is birationally isomorphic to a smooth complete intersection of n-2 diagonal quadrics in Pⁿ⁺². We also describe an action of the 2-elementary abelian group 2ⁿ⁺² on this family via Cremona transformations in Pⁿ.

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