Curves of twice the minimal class on principally polarized abelian varieties. (English) Zbl 0644.14014

The author studies a special type of principally polarized abelian varieties (PPAV). Due to Kanev every PPAV admits a Prym-Tjurin presentation, which consists of a morphism \(v: N\to X\) of a smooth, complete irreducible curve N to the PPAV X of dimension g such that \(v_*[N]=m[\vartheta]^{g-1}/(g-1)!\) where \(m\geq 1\) is an integer and \(\vartheta\) is the polarization divisor. The case of \(m=1\) corresponds to Jacobian varieties and the author treats here the next simplest case, \(m=2\), which includes the usual Prym varieties as an extreme type. The author classifies all possible types of the image curve \(C=v(N)\). More detailed study of the moduli is an interesting problem in the future. The method used here is standard.
Reviewer: Y.Namikawa


14K10 Algebraic moduli of abelian varieties, classification
14H10 Families, moduli of curves (algebraic)
14K30 Picard schemes, higher Jacobians
14C20 Divisors, linear systems, invertible sheaves
14K05 Algebraic theory of abelian varieties
14H40 Jacobians, Prym varieties