Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

We present results from an inductive algebraic approach to the systematic construction and classification of the ‘lowest-level’ CY3 spaces defined as zeroes of polynomial loci associated with reflexive polyhedra, derived from suitable vectors in complex projective spaces. These CY3 spaces may be sorted into ‘chains’ obtained by combining lower-dimensional projective vectors classified previousl...