Computing Green Currents via the Heat Kernel

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 08/2000

MSC 2000

32Q15 Kähler manifolds

32J27 Compact Kähler manifolds: generalizations, classification

14C17 Intersection theory, characteristic classes, intersection multiplicities

Let X be a compact Kähler manifold. We show that there exists a unique Green current g_Y for any cycle Y in X. We show that the current g_Y is a form with L¹-coefficients. The heat kernel applied to the Dirac distribution associated with Y plays a central role in this construction. Furthermore, we show how these Green currents fit into intersection theory. Finally, we compute this canonical current for some examples.

Keywords: Kähler manifold, cycle, Green current, heat kernel, intersection theory

Notes:
This paper is part of a project together with J. Kramer, W. Gubler, D. Roessler on arithmetic intersection theory