S ep 1 99 9 Some properties of second order theta functions on Prym varieties
نویسنده
چکیده
Let P ∪P ′ be the two component Prym variety associated to anétale double cover˜C → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ 0 | 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˜C. We show that the base locus of the subseries of divisors containing˜C ⊂ P ′ is exactly the curve˜C. We also prove canonical isomorphisms between some subseries of |2Ξ 0 | and |2Ξ ′ 0 | and some subseries of second order theta divisors on the Jacobian of C.
منابع مشابه
1 8 M ay 1 99 9 Some properties of second order theta functions on Prym varieties
Let P ∪P ′ be the two component Prym variety associated to anétale double cover˜C → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ 0 | 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˜C. We show that the base locus of the subseries of divisors containing˜C ⊂ P ′ is exactly the curve˜C. ...
متن کاملSome properties of second order theta functions on Prym varieties
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 exactly the curve C̃. We...
متن کاملS ep 2 00 8 Singularities of the Prym Theta Divisor Sebastian
For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds, and Prym varieties of dimension five, are also considered.
متن کاملThe Curve of “prym Canonical” Gauss Divisors on a Prym Theta Divisor
Introduction: A good understanding of the geometry of a theta divisor Θ of a principally polarized abelian variety (A,Θ) requires a knowledge of properties of its canonical linear system, the Gauss linear system |OΘ(Θ)|. A striking feature of the theta divisor Θ(C) of the Jacobian of a curve C is that the dual of the branch divisor of the associated Gauss map γΘ on Θ, is not a hypersurface as e...
متن کامل1 1 M ay 2 00 4 Singularities of the Prym Theta Divisor
For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds, and Prym varieties of dimension five, are also considered.
متن کامل