On Abel’s Hyperelliptic Curves

Torsten Ekedahl ()
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Torsten Ekedahl: Stockholm University, Department of Mathematics

A chapter in The Legacy of Niels Henrik Abel, 2004, pp 441-466 from Springer

Abstract: Abstract In this note we discuss a class of hyperelliptic curves introduced by Abel in an 1826 paper. After some indications of the context in which he introduced them and a description of his main result we give some results on the moduli space of such curves. In particular we compute the dimension of it at each of its points as well as giving a combinatorial formula for the number of components.

Keywords: Line Bundle; Hyperelliptic Curve; Branch Locus; Weierstrass Point; Cartier Divisor (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18908-1_12

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DOI: 10.1007/978-3-642-18908-1_12

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