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In this paper we consider moduli spaces of coherent systems on an ellipticcurve. We compute their Hodge polynomials and determine their birational typesin some cases. Moreover we prove that certain moduli spaces of coherent systemsare isomorphic. This last result uses the Fourier-Mukai transform of coherentsystems introduced by Hern\'andez Ruiperez and Tejero Prieto.

Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves