  In oxide heterostructures, different materials are integrated into a single
artificial crystal, resulting in a breaking of inversion-symmetry across the
heterointerfaces. A notable example is the interface between polar and
non-polar materials, where valence discontinuities lead to otherwise
inaccessible charge and spin states. This approach paved the way to the
discovery of numerous unconventional properties absent in the bulk
constituents. However, control of the geometric structure of the electronic
wavefunctions in correlated oxides remains an open challenge. Here, we create
heterostructures consisting of ultrathin SrRuO$_3$, an itinerant ferromagnet
hosting momentum-space sources of Berry curvature, and LaAlO$_3$, a polar
wide-bandgap insulator. Transmission electron microscopy reveals an atomically
sharp LaO/RuO$_2$/SrO interface configuration, leading to excess charge being
pinned near the LaAlO$_3$/SrRuO$_3$ interface. We demonstrate through
magneto-optical characterization, theoretical calculations and transport
measurements that the real-space charge reconstruction modifies the
momentum-space Berry curvature in SrRuO$_3$, driving a reorganization of the
topological charges in the band structure. Our results illustrate how the
topological and magnetic features of oxides can be manipulated by engineering
charge discontinuities at oxide interfaces.
