Deformations and moduli of irregular canonical covers with K2=4pg−8

Abstract

In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying K2=4pg−8, for any even integer pg≥4. These surfaces also have unbounded irregularity q. We carry out our study by investigating the deformations of the canonical morphism φ:X→PN, where φ is a quadruple Galois cover of a smooth surface of minimal degree. These canonical covers are classified in Gallego and Purnaprajna (Trans Am Math Soc 360(10):5489-5507, 2008) into four distinct families, one of which is the easy case of a product of curves.