Abelian fourfold of Mumford-type and Kuga-Satake varieties
نویسندگان
چکیده
منابع مشابه
Abelian Varieties of Weil Type and Kuga-satake Varieties
We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.
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Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of Kuga-Satake varieties. The Hodge conjecture is discussed in section 2. An excellent survey of the Hodge conjecture for abelian varieties is [...
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The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate vari...
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The Kuga-Satake construction [3] associates to a polarized Hodge structure H of weight 2 with h2,0 = 1 an abelian variety A which satisfies the property that H is a sub-Hodge structure of Hom (H1(A),H1(A)). The construction is very tricky and intriguing geometrically: one first associates to the lattice (H,<,>) its Clifford algebra C(H), which is again a lattice. Then one constructs a complex s...
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Contents 1. Introduction 2 2. Prym varieties for covers of curves 3 3. Galois covers 8 4. Degree two covers 10 5. Covers of degree three 13 6. Covers of degree four 15 6.1. The cyclic case 15 6.2. The Klein case 17 7. The dihedral case 22 7.1. The bigonal construction 34 8. The alternating case 37 8.1. The trigonal construction for the case A 4 43 9. The symmetric case 44 9.1. The classical cas...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2000
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(00)80024-5