Abstract

In this talk, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying , for any even integer . These surfaces also have unbounded irregularity . We carry out our study by investigating the deformations of the canonical morphism , where is a quadruple Galois cover of a smooth surface of minimal degree. As a result, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality , with an irreducible component that has a proper "quadruple" sublocus where the degree of the canonical morphism jumps up. The existence of jumping subloci is a contrast with the moduli of surfaces with , studied by Horikawa. These irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus , for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational.

Link Information

https://us02web.zoom.us/j/81528379233?pwd=MVU4RW53RGVuMWpITFBzSVVMTGF4dz09