On certain families of elliptic curves in projective space

Igor V. Dolgachev

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On certain families of elliptic curves in projective space

Igor V. Dolgachev

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Abstract

We study families of elliptic curves of degree n+1 in $P^n$ 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 $P^{n+2}$. We also describe an action of the 2-elementary abelian group $2^{n+2}$ on this family via Cremona transformations in $P^n$.

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BibTeX RIS

Igor V. Dolgachev. 2002-06-13. On certain families of elliptic curves in projective space. https://arxiv.org/abs/math/0205197

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