20260203 Noncommutative Hilbert schemes and a Springer resolution

After recalling basic ideas of noncommutative algebraic geometry, we construct moduli spaces for one-sided ideals in noncommutative formal power series rings, called (punctual) noncommutative Hilbert schemes. For these schemes, we construct affine pavings and a Springer-type resolution of singularities, which allows us to determine their Borel-Moore- and intersection Betti numbers. All constructions are based on explicit linear algebra methods.