A characterization of bielliptic curves and applications to their moduli spaces

Abstract.We deal with the covers of degree 4 naturally associated to a bielliptic curve of genus g≥6, giving a proof of the unirationality of the moduli space ?gbe of such curves, of the rationality of the Hurwitz scheme ℌbe4,g of bielliptic curves of even genus g, whereas, when g is odd, we construct a finite map ℂ2g-2→?gbe and compute its degree.