Real rectifiable currents, holomorphic chains and algebraic cycles

Anti-holomorphic Multiplication and a Real Algebraic Modular Variety

An anti-holomorphic multiplication by the integers Od of a quadratic imaginary number field, on a principally polarized complex abelian variety AC is an action of Od on AC such that the purely imaginary elements act in an anti-holomorphic manner. The coarse moduli space XR of such A (with appropriate level structure) is shown to consist of finitely many isomorphic connected components, each of ...

Leaf superposition property for integer rectifiable currents

We consider the class of integer rectifiable currents without boundary in Rn × R satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.

Pseudo-holomorphic and Algebraic Classifications

Almost all known restrictions on the topology of nonsingular real algebraic curves in the projective plane are also valid for a wider class of objects: real pseudo-holomorphic curves. It is still unknown if there exists a nonsingular real pseudo-holomorphic curve not isotopic in the projective plane to a real algebraic curve of the same degree. In this article, we focus our study on symmetric r...

Residue Currents of Holomorphic Morphisms

Given a generically surjective holomorphic vector bundle morphism f : E → Q, E and Q Hermitian bundles, we construct a current R with values in Hom (Q,H), where H is a certain derived bundle, and with support on the set Z where f is not surjective. The main property is that if φ is a holomorphic section of Q, and Rφ = 0, then locally fψ = φ has a holomorphic solution ψ. In the generic case also...

Rectifiable and Flat G Chains in a Metric Space