منابع مشابه
Periods of Limit Mixed Hodge Structures
The first goal of this paper is to explain some important results of Wilfred Schmid from his fundamental paper [30] in which he proves very general results which govern the behaviour of the periods of a of smooth projective variety Xt as it degenerates to a singular variety. As has been known since classical times, the periods of a smooth projective variety sometimes contain significant informa...
متن کاملSome remarks on limit mixed Hodge structures and spectrum
In this note we clarify some subtle points on the limit mixed Hodge structures and on the spectrum. These are more or less well-known to the specialists, but do not seem to be stated explicitly in the literature. However, as they do not seem to be obvious to the beginners, we consider them to be worth writing down explicitly. The general constructions are exemplified by considering the isolated...
متن کاملNonabelian mixed Hodge structures
We propose a definition of “nonabelian mixed Hodge structure” together with a construction associating to a smooth projective variety X and to a nonabelian mixed Hodge structure V , the “nonabelian cohomology of X with coefficients in V ” which is a (pre-)nonabelian mixed Hodge structure denoted H = Hom(XM , V ). We describe the basic definitions and then give some conjectures saying what is su...
متن کاملArithmetic Mixed Hodge Structures
We give a formalism of arithmetic mixed Hodge structures which are recently studied by M. Green [13], [14] and M. Asakura [1], and are named by them. This notion became necessary for us to describe the image of the Abel-Jacobi map for a generic hypersurface (inspired by previous work of M. Green [12] and C. Voisin [28]), and also to prove the following variant of results of D. Mumford [17] and ...
متن کاملMixed Hodge Structures
such that F p(V ) ⊃ F p+1(V ) (resp. Fp(V ) ⊂ Fp+1(V ) for all p ∈ Z. The filtration is called finite if there exist integers m > n such that Fm(V ) = 0 and Fn(V ) = V (resp. Fm(V ) = V , Fn(V ) = 0). Observe that given a decreasing filtration {F p(V )} we can form an increasing filtration Fp(V ) := F−p(V ). In the remainder of this section we will work exclusively with decreasing filtration so...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2002
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2002.v2002.n1.a3