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Abstract
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The size of the automorphism group of a compact Riemann surface of
genus is
bounded by
.
Curves with automorphism group of size equal to this bound are called Hurwitz curves.
In many cases the automorphism group of these curves is the projective special linear
group
.
We present a decomposition of the Jacobian varieties for all curves of this type and
prove that no such Jacobian variety is simple.
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Keywords
Jacobian varieties, Hurwitz curves, projective special
linear group, representation theory
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Mathematical Subject Classification 2010
Primary: 14H40, 14H37, 20G05
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Milestones
Received: 5 February 2015
Revised: 8 July 2015
Accepted: 20 July 2015
Published: 6 July 2016
Communicated by Nigel Boston
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