The Hodge conjecture for general Prym varieties
نویسندگان
چکیده
منابع مشابه
The Hodge Conjecture for General Prym Varieties
We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity component of the kernel of the norm homomorphism N : J(C) → J(D) between the Jacobians of the curves. This is an abelian variety polarised by the restriction of the canonical polarisation on J(C); we de...
متن کاملKuga-satake Varieties and the Hodge Conjecture
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 [...
متن کاملSome Remarks on the Hodge Conjecture for Abelian Varieties
Let X be a smooth complex projective variety of dimension g. A Hodge class of degree 2d on X is, by definition, an element of H(X,Q)∩H(X). The cohomology class of an algebraic subvariety of codimension d of X is a Hodge class of degree 2d. The classical Hodge conjecture states that any Hodge class on X is algebraic, i.e., a Q-linear combination of classes of algebraic subvarieties of X. Lefsche...
متن کاملA counterexample to the Hodge conjecture for Kähler varieties
H(X,C) = ⊕p+q=kH (X). A class α ∈ H(X,Q) is said to be a rational Hodge class if its image in H(X,C) belongs to H(X). As is well known, the classes which are Poincaré dual to irreducible algebraic subvarieties of codimension p of X are degree 2p Hodge classes. The Hodge conjecture asserts that any rational Hodge class is a combination with rational coefficients of such classes. In the case of a...
متن کاملAn Inductive Approach to the Hodge Conjecture for Abelian Varieties
Let X be a smooth complex projective variety of dimension g. A Hodge class of degree 2d on X is, by definition, an element of H(X,Q)∩H(X). The cohomology class of an algebraic subvariety of codimension d of X is a Hodge class of degree 2d. The original Hodge conjecture states that any Hodge class on X is algebraic, i.e., a Q-linear combination of classes of algebraic subvarieties of X. Lefschet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2002
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-01-00303-4