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Ownership is a powerful concept to structure the object store and to control aliasing and modifications of objects. This paper presents an ownership type system for a Java-like programming language with generic types. Like our earlier Universe type system, Generic Universe Types enforce the owner-as-modifier discipline. This discipline does not restrict aliasing, but requires modifications of an object to be initiated by its owner. This allows owner objects to control state changes of owned objects, for instance, to maintain invariants. Generic Universe Types require a small annotation overhead and provide strong static guarantees. They are the first type system that combines the owner-as-modifier discipline with type genericity.