Synthetic data generation via generative modeling has recently become a prominent research field in genomics, with applications ranging from functional sequence design to high-quality, privacy-preserving artificial in silico genomes. Following a body of work on Artificial Genomes (AGs) created via various generative models trained with raw genomic input, we propose a conceptually different approach to address the issues of scalability and complexity of genomic data generation in very high dimensions. Our method combines dimensionality reduction, achieved by Principal Component Analysis (PCA), and a Generative Adversarial Network (GAN) learning in this reduced space. We compare the quality of AGs generated by our approach with AGs generated by the established models and report improvements on capturing population structure and linkage disequilibrium.