Deformation of canonical morphisms and the moduli of surfaces of general type

الأصل · EN

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different c₁² and χ. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces M₍ₓ',₀,y₎ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.