The Kodaira dimension of the moduli space of Prym varieties
نویسندگان
چکیده
منابع مشابه
The Kodaira Dimension of the Moduli Space of Prym Varieties
Prym varieties provide a correspondence between the moduli spaces of curves and abelian varieties Mg and Ag−1, via the Prym map Pg : Rg → Ag−1 from the moduli space Rg parameterizing pairs [C, η], where [C] ∈ Mg is a smooth curve and η ∈ Pic(C)[2] is a torsion point of order 2. When g ≤ 6 the Prym map is dominant and Rg can be used directly to determine the birational type ofAg−1. It is known t...
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Definition 1.1. Let L be a line bundle on a normal, irreducible, projective variety. Then the Iitaka dimension of L is defined to be the maximum dimension of the image of πm for m ⊕ N(X, L) provided N(X, L) ∈= 0. If N(X, L) = 0, then the Iitaka dimension of L is defined to be −→. When X is smooth, the Kodaira dimension of X is defined to be the Iitaka dimension of its canonical bundle KX . If X...
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This survey discusses the geometry of the moduli space of Prym varieties. Several applications of Pryms in algebraic geometry are presented. The paper begins with with a historical discussion of the life and achievements of Friedrich Prym. Topics treated in subsequent sections include singularities and Kodaira dimension of the moduli space, syzygies of Prym-canonical embedding and the geometry ...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2010
ISSN: 1435-9855
DOI: 10.4171/jems/214