Modeling the relationships among variables has become increasingly important, particularly in high-dimensional multivariate time series forecasting tasks. However, most existing methods primarily focus on capturing coarse-grained correlations between variables, overlooking a finer and more dynamic aspect: the variable interactions often manifest differently as time progresses. To address this limitation, we propose FACT, an Fine-grained Across-variable Convolution architecture for multivariate Time series forecasting that explicitly models fine-grained variable interactions from both the time and frequency domains. Technically, we introduce a depth-wise convolution block DConvBlock, which leverages a depth-wise convolution architecture with channel-specific kernels to model dynamic variable interactions at each granularity. To further enhance efficiency, we reconfigure the original one-dimensional variables into a two-dimensional space, reducing the variable distance and the required model layers. Then DConvBlock incorporates multi-dilated 2D convolutions with progressively increasing dilation rates, enabling the model to capture fine-grained and dynamic variable interactions while efficiently attaining a global reception field. Extensive experiments on twelve benchmark datasets demonstrate that FACT not only achieves state-of-the-art forecasting accuracy but also delivers substantial efficiency gains, significantly reducing both training time and memory consumption compared to attention mechanism.