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• W1767218978 abstract "Let the threefold X be a general smooth conic bundle over the projective plane P(2), and let (J(X), Theta) be the intermediate jacobian of X. In this paper we prove the existence of two natural families C(+) and C(-) of curves on X, such that the Abel-Jacobi map F sends one of these families onto a copy of the theta divisor (Theta), and the other -- onto the jacobian J(X). The general curve C of any of these two families is a section of the conic bundle projection, and our approach relates such C to a maximal subbundle of a rank 2 vector bundle E(C) on C, or -- to a minimal section of the ruled surface P(E(C)). The families C(+) and C(-) correspond to the two possible types of versal deformations of ruled surfaces over curves of fixed genus g(C). As an application, we find parameterizations of J(X) and (Theta) for certain classes of Fano threefolds, and study the sets Sing(Theta) of the singularities of (Theta)." @default.
• W1767218978 created "2016-06-24" @default.
• W1767218978 creator A5064784838 @default.
• W1767218978 date "1999-01-01" @default.
• W1767218978 modified "2023-10-16" @default.
• W1767218978 title "Minimal sections of conic bundles" @default.
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