Summands of theta divisors on Jacobians
نویسندگان
چکیده
منابع مشابه
On the Singularities of Theta Divisors on Jacobians
The theta divisor Θ of the Jacobian variety of a complex curve X is best viewed as a divisor inside the component Pic(X) consisting of (isomorphism classes of) line bundles of degree g−1. Then a line bundle L belongs to Θ if and only if it has non-zero sections. Riemann proved that the multiplicity of Θ at a point L is equal to dimH(X;L) − 1. Kempf ([Ke]) obtained a geometric proof of Riemann’s...
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Let A be a principally polarized abelian variety of dimension four and let Θ ⊂ A be a symmetric theta-divisor, which we assume to be smooth. Using the Hodge structure on H(Θ) we associate to A two abelian subvarieties J(K) ⊂ J(H) of the intermediate jacobian J(Θ) of Θ of dimensions five and nine respectively. We show that J(H) is generated by the image under the Abel-Jacobi map of the family F ...
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The Schottky problem is the problem of finding necessary and sufficient conditions for a principally polarized abelian variety (ppav) to be a product of jacobians of smooth curves. Let (P,Ξ) be a ppav of dimension p ≥ 4 with Ξ a symmetric theta divisor on P . The elements of Γ = H(P, 2Ξ) are symmetric, hence their multiplicities at the origin are always even. Let Γ0 ⊂ Γ be the subvector space o...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2020
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x20007204