Algebra & Number Theory
- Algebra Number Theory
- Volume 12, Number 9 (2018), 2123-2150.
A formula for the Jacobian of a genus one curve of arbitrary degree
We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree , an alternating matrix of quadratic forms in variables, that represents the invariant differential. We then exhibit the invariants we need as homogeneous polynomials of degrees and in the coefficients of the entries of this matrix.
Algebra Number Theory, Volume 12, Number 9 (2018), 2123-2150.
Received: 30 August 2017
Revised: 15 June 2018
Accepted: 15 July 2018
First available in Project Euclid: 5 January 2019
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Fisher, Tom. A formula for the Jacobian of a genus one curve of arbitrary degree. Algebra Number Theory 12 (2018), no. 9, 2123--2150. doi:10.2140/ant.2018.12.2123. https://projecteuclid.org/euclid.ant/1546657276