This research constructs algebraic varieties and compact manifolds with specific group properties, suggesting foundational advancements in geometry.
Key Points
The study aims to construct algebraic varieties and compact manifolds whose automorphism and diffeomorphism groups exhibit specified properties related to nilpotent groups.
Analyzed algebraically closed fields and natural numbers for constructions.
Developed models for algebraic varieties with specified birational automorphism groups.
Constructed compact manifolds whose diffeomorphism groups match given criteria.
Established constructions for algebraic varieties with birational automorphism groups containing finite nilpotent groups.
Showed similar constructions exist for compact manifolds with specified diffeomorphism groups.
Confirmed the sharpness of the results in characteristic zero.