Reduced-dimensional supervector representations are shown to outperform their supervector counterparts in a variety of speaker recognition tasks. They have been exploited in automatic language verification (ALV) tasks as well but, to the best of our knowledge, their performance is comparable with their supervector counterparts. This paper demonstrates that nonlinear polynomial kernel support vector machines (SVMs) trained with low dimensional supervector representations almost halve the equal error rate (EER) of the SVMs trained with supervectors. Principal component analysis (PCA) is typically used for dimension reduction in ALV. Nonlinear kernel SVMs then implicitly transform these low dimensional representations onto higher-dimensional spaces. Unlike linear kernels, the transformations onto high dimensional feature spaces exploit the language-specific dependencies across different input dimensions. Mapping input training examples onto higher dimensional feature spaces is known to be generally effective when the number of instances is much larger than the input dimensionality. Our experiments demonstrate that fifth-order polynomial kernel SVMs trained with low dimensional representations reduce the EER by 56% relative when compared to linear SVMs trained with supervectors, and by 40% relative to nonlinear SVMs trained with supervectors. Furthermore, they also reduce the EER of linear kernel SVMs trained with the low dimensional representations by 71% relative.