A formula for the Jacobian of a genus one curve of arbitrary degree
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Fisher, Tom
Abstract
We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree n <= 4 to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree n, an n x 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.
Description
Keywords
elliptic curves, invariant theory, higher secant varieties
Journal Title
ALGEBRA & NUMBER THEORY
Conference Name
Journal ISSN
1937-0652
1944-7833
1944-7833
Volume Title
12
Publisher
Mathematical Sciences Publishers