منابع مشابه
Abel Maps and Presentation Schemes
We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding p...
متن کاملNaturality of Abel maps
We give a combinatorial characterization of nodal curves admitting a natural (i.e. compatible with and independent of specialization) d-th Abel map for any d ≥ 1. Let X be a smooth projective curve and d a positive integer; the classical d-th Abel map of X , αX : X d −→ PicX , associates to (p1, . . . , pd) ∈ X the class of the line bundle OX(p1 + . . .+ pd) in Pic d X . Such a morphism has goo...
متن کاملAbel maps and limit linear series
Definition 2.1. Fix integers d and r. A limit (linear) series on X of degree d and rank r is a collection consisting of an invertible sheaf L on X of degree d on Y and degree 0 on Z, and vector subspaces Vi ⊆ Γ(X,L) of dimension r + 1, for each i = 0, . . . , d, such that φ(Vi) ⊆ Vi+1 and φi(Vi+1) ⊆ Vi for each i. Given a limit series (L, V0, . . . , Vd), we denote by V Y,0 i the subspace of Vi...
متن کاملOn Abel Maps of Stable Curves
We construct Abel maps for a stable curve X. Namely, for each one-parameter deformation of X to a smooth curve, having regular total space, and each integer d ≥ 1, we construct by specialization a map αdX : Ẋ d → P d X , where Ẋ ⊆ X is the smooth locus, and P d X is the moduli scheme for balanced line bundles on semistable curves over X. For d = 1, we show that αX extends to a map α 1 X : X → P...
متن کاملArithmetic Hodge Structure and Higher Abel-jacobi Maps
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford in...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2000
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870008827199