منابع مشابه
The Hodge Conjecture
In the twentieth century, mathematicians developed very eeective methods for understanding the general shape of smooth geometric objects called manifolds. These methods consist of various cohomology theories, which form a large and very active part of current mathematical research. Very loosely speaking, the Hodge Conjecture predicts that, for manifolds that can be described by polynomial equat...
متن کاملThe Hodge Conjecture
We recall that a pseudo complex structure on a C∞-manifold X of dimension 2N is a C-module structure on the tangent bundle TX . Such a module structure induces an action of the group C∗ on TX , with λ ∈ C∗ acting by multiplication by λ. By transport of structures, the group C∗ acts also on each exterior power ∧TX , as well as on the complexified dual Ω := Hom(∧TX ,C). For p+ q = n, a (p, q)-for...
متن کاملIntroduction to the Hodge Conjecture
These are notes from a talk introducing the Hodge conjecture to undergraduates attending the 2009 Clemson REU. The description given here of the Hodge conjecture was the author’s attempt to bring the conjecture down to a reasonably understandable level to undergraduates. As such, liberties have been taken with the accuracy and generality of some of the statements. Please keep this in mind when ...
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 کاملVanishing Cycles and the Generalized Hodge Conjecture
Let X be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of X is ample. Using the cylinder homomorphism associated with the family of complete intersections contained in X, we prove that the vanishing cycles in the middle homology group of X are represented by topological cycles whose support is contained in a pr...
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ژورنال
عنوان ژورنال: Journal of Algebraic Geometry
سال: 2005
ISSN: 1056-3911,1534-7486
DOI: 10.1090/s1056-3911-04-00378-9