The Hodge existence theorem. I

The Hodge theorem for Riemannian manifolds

On 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...

Hodge-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...

The 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.

An Equilibrium Existence Theorem

Bewley 14, Theorem l] proved an infinite dimensional equilibrium existence theorem which is a significant extension of the classical finite dimensional theorem of Arrow and Debreu [ 11. The assumptions on technology and preferences are natural and applicable in a wide variety of cases. The proof is based on a limit argument that makes direct use of the existence of equilibrium in the finite dim...