Some Properties of Second Order Theta Functions o Prym Varieties |
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| Authors: | E Izadi C Pauly |
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| Institution: | 1. Department of Mathematics, Boyd Graduate Studies Research Center, University of Georgia, Athens, GA 30602-7403, USA;2. Laboratoire J.-A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France |
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| Abstract: | Let P ∪ P′ be the two component Prym variety associated to an étale double cover C̃ → C of a non-hyperelliptic curve of genus g ≥6 and let |2Ξ0| and |2Ξ′0| be the linear systems of second order theta divisors on P and P′ respectively. The component P′ contains canonically the Prym curve C̃. We show that the base locus of the subseries of divisors containing C̃ ⊂ P′ is exactlythe curve C̃. We also prove canonical isomorphisms between some subseries of |2Ξ0| and |2Ξ′0| and some subseries of second order theta divisors on the Jacobian of C. |
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