منابع مشابه
Hodge Correlators Ii
We define Hodge correlators for a compact Kähler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real mixed Hodge structure on the rational homotopy type of X. The Hodge correlators provide a canonical linear map from the cyclic homomogy of the cohomology algebra...
متن کاملOn the Existence of Nontrivial Threefolds with Vanishing Hodge Cohomology
We analyze the structure of the algebraic manifolds Y of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h 0(Y,OY ) > 1, by showing the deformation invariant of some open surfaces. Secondly, we show when a smooth threefold with nonconstant regular functions satisfies the vanishing Hodge cohomology. As an application, we prove the existence of nonaffine and nonproduct threefolds Y with t...
متن کاملHodge-theoretic obstruction to the existence of quaternion algebras
This paper gives a necessary criterion in terms of Hodge theory for representability by quaternion algebras of certain 2-torsion classes in the unramified Brauer group of a complex function field. This criterion is used to give examples of threefolds with unramified Brauer group elements which are the classes of biquaternion division algebras. DOI: https://doi.org/10.1112/S0024609302001546 Post...
متن کاملThe Local Theory of Elliptic Operators and the Hodge Theorem
In this paper, we develop the local theory of elliptic operators with a mind to proving the Hodge Decomposition Theorem. We then deduce a few of its corollaries including, for compact, oriented manifolds, Poincaré Duality and finite-dimensionality of the de Rham cohomology groups.
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: Advances in Mathematics
سال: 1971
ISSN: 0001-8708
DOI: 10.1016/0001-8708(71)90024-7