A formula for the Jacobian of a genus one curve of arbitrary degree

Abstract

We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree $n\le 4$ to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree $n$, an $n\times n$ alternating matrix of quadratic forms in $n$ variables, that represents the invariant differential. We then exhibit the invariants we need as homogeneous polynomials of degrees $4$ and $6$ in the coefficients of the entries of this matrix.

26 pages

References in corpus (2)

• The invariants of a genus one curve
• Geometric syzygies of elliptic normal curves and their secant varieties

Cited by in corpus (1)

• Feigin-Odesskii brackets, syzygies, and Cremona transformations