Language variety identification aims at labelling texts in a native language (e.g. Spanish, Portuguese, English) with its specific variation (e.g. Argentina, Chile, Mexico, Peru, Spain; Brazil, Portugal; UK, US). In this work we propose a low dimensionality representation (LDR) to address this task with five different varieties of Spanish: Argentina, Chile, Mexico, Peru and Spain. We compare our LDR method with common state-of-the-art representations and show an increase in accuracy of ~35%. Furthermore, we compare LDR with two reference distributed representation models. Experimental results show competitive performance while dramatically reducing the dimensionality --and increasing the big data suitability-- to only 6 features per variety. Additionally, we analyse the behaviour of the employed machine learning algorithms and the most discriminating features. Finally, we employ an alternative dataset to test the robustness of our low dimensionality representation with another set of similar languages.