Accurate mapping of biomolecular information onto tissue section image coordinates is a fundamental requirement in spatial multi-omics analysis， where the precision of nuclei segmentation critically determines the accuracy of target molecule localization. However， existing segmentation methods frequently produce suboptimal outcomes due to challenges such as highly heterogeneous nuclear morphology， complex tissue architecture， and densely packed cellular regions， all of which compromise the reliability of downstream spatial genomics analyses. To overcome these challenges， FFVM-UKAN， a novel encoder-decoder architecture， is proposed. This architecture integrates shallow Visual State Space modules for feature extraction with a deep tokenized Kolmogorov-Arnold Network for feature refinement. Additionally， a Parallel Frequency Domain Learnable Module is incorporated to significantly enhance skip connections by effectively capturing fine-grained frequency-level features essential for high-precision nuclei segmentation. The proposed method achieved a mean Intersection over Union （mIoU） of 69.09% and a Dice coefficient of 81.72% on the MoNuSeg dataset， and 85.95% and 92.45% respectively on an in-house dataset. Further validation using the 10X Genomics human liver dataset for gene-to-nuclei mapping yielded an accuracy of 90.63%. Experimental results demonstrate that the proposed approach delivers superior nuclei segmentation accuracy and robust model generalization. This enables highly precise gene-to-nuclei mapping， underscoring the significant potential of this method to advance spatial multi-omics research and its applications.