Singularities of the Prym theta divisor
نویسندگان
چکیده
منابع مشابه
1 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 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.
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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...
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Let (P,Ξ) be the naturally polarized model of the Prym variety associated to the étale double cover π : C̃ → C of smooth connected curves, where Ξ ⊂ P ⊂ Pic2g−2(C̃), and g(C) = g. If L is any “non exceptional” singularity of Ξ, i.e. a point L on Ξ ⊂ Pic2g−2(C̃) such that h0(C̃, L) ≥ 4, but which cannot be expressed as π∗(M)(B) for any line bundle M on C with h0(C,M) ≥ 2 and effective divisor B ≥ 0 ...
متن کاملThe Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor
The object of study here is the singular locus of the theta divisor Θ of a principally polarized abelian variety (X,Θ). The special case when (X,Θ) is the Jacobian of a curve C shows that this is meaningful: singularities of Θ are closely related to the existence of special linear systems on the curve C and for curves of genus g ≥ 4 the divisor Θ is always singular. But for the general principa...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2009
ISSN: 0003-486X
DOI: 10.4007/annals.2009.170.163