Two-dimensional moduli spaces of vector bundles over Kodaira surfaces

TL;DR

This paper investigates the structure of two-dimensional moduli spaces of stable rank-2 vector bundles on primary Kodaira surfaces, showing they are themselves primary Kodaira surfaces and exploring conditions for universal bundles.

Contribution

It establishes that such moduli spaces are primary Kodaira surfaces and characterizes their topological relationship when a universal bundle exists.

Findings

Moduli spaces are primary Kodaira surfaces.

Existence of universal bundle implies homeomorphism up to covers.

Results apply in the non-filtrable range.

Abstract

We prove that any two-dimensional moduli space of stable 2-vector bundles, in the non-filtrable range, on a primary Kodaira surface is a primary Kodaira surface. If a universal bundle exists, then the two surfaces are homeomorphic up to unramified covers.