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Lacunary Wronskians on genus one curves

✍ Scribed by Greg W. Anderson

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 178 KB
Volume: 115
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2004.11.001

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✦ Synopsis

Let X be a nonsingular projective curve of genus one defined over an algebraically closed field of characteristic 0. Let D be a divisor of X of degree n > 1 and let O be a (closed) point of X. As is well known, there exists a unique morphism

Our main result is a simple explicit description of the map D,O in terms of Wronskians and certain Wronskian-like determinants lacunary in the sense that derivatives of some orders are skipped. Further, for n = 2, 3 we interpret our main result as a syzygy from classical invariant theory, thus reconciling our work with a circle of ideas treated in two papers by Weil and a recent paper by An, Kim, Marshall, Marshall, McCallum and Perlis.

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