Abstract
AbstractThe second chapter gives the definition of Prym varieties and derives the properties which are needed in the subsequent chapters. For any finite cover of smooth projective curves f : C˜ → C the Prym variety P(f) = P(C˜∕C) is defined to be the complementary abelian subvariety of f ∗ J in \(\widetilde J\) with respect to the canonical polarization of \(\widetilde J\). Here J and \(\widetilde J\) denote the Jacobian varieties of C and \(\widetilde C\) respectively.So our notion of Prym variety is more general than the original notion introduced by Mumford. We call his more special Prym varieties principally polarized Prym varieties. Hence for us, Prym varieties are not necessarily principally polarized.
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