On certain families of elliptic curves in projective space

الأصل · EN

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.