In this paper we shall prove two theorems concerning holomorphic mappings of large open sets of ℂk into algebraic varieties. Both are in response to well-known outstanding problems, and we feel that… Expand

In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the… Expand

Given the data (X,L, ζ) where X is a smooth 2n-dimensional algebraic variety, L → X is a very ample line bundle and ζ ∈ Hg(X)prim is a primitive Hodge class, we shall define an analytic invariant

Talk given at the "Algebraic Geometry in Mexico" conference taking place at Puerta Escondido, December 2 - 7, 2018. Partly based on work in progress with Mark Green, Radu Laza and Colleen Robles.