HODGE THEORY AND GEOMETRY

Hodge Theory and Geometry

This expository paper is an expanded version of a talk given at the joint meeting of the Edinburgh and London Mathematical Societies in Edinburgh to celebrate the centenary of the birth of Sir William Hodge. In the talk the emphasis was on the relationship between Hodge theory and geometry, especially the study of algebraic cycles that was of such interest to Hodge. Special attention will be pl...

Anabelian Geometry in the Hodge-Arakelov Theory of Elliptic Curves

The purpose of the present manuscript is to survey some of the main ideas that appear in recent research of the author on the topic of applying anabelian geometry to construct a “global multiplicative subspace”— i.e., an analogue of the well-known (local) multiplicative subspace of the Tate module of a degenerating elliptic curve. Such a global multiplicative subspace is necessary to apply the ...

Hodge Theory and Representation Theory

Residues and Hodge theory

We discuss some basic applications of higher dimensional residues as presented in [7] and [8, Chap. V].

N = 1 Special Geometry , Mixed Hodge Variations and Toric Geometry

We study the superpotential of a certain class of N = 1 supersymmetric type II compactifications with fluxes and D-branes. We show that it has an important two-dimensional meaning in terms of a chiral ring of the topologically twisted theory on the world-sheet. In the open-closed string B-model, this chiral ring is isomorphic to a certain relative cohomology group V , which is the appropriate m...