caa a22 4500 463203151 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00200-006-0030-9 doi (NATIONALLICENCE)springer-10.1007/s00200-006-0030-9 Hyperelliptic curves with reduced automorphism group A 5 [Elektronische Daten] [David Sevilla, Tanush Shaska] We study genus g hyperelliptic curves with reduced automorphism group A 5 and give equations y 2=f(x) for such curves in both cases where f(x) is a decomposable polynomial in x 2 or x 5. For any fixed genus the locus of such curves is a rational variety. We show that for every point in this locus the field of moduli is a field of definition. Moreover, there exists a rational model y 2=F(x) or y 2=x F(x) of the curve over its field of moduli where F(x) can be chosen to be decomposable in x 2 or x 5. While similar equations have been given in (Bujalance etal. in Mm. Soc. Math. Fr. No. 86, 2001) over $${\mathbb R}$$ , this is the first time that these equations are given over the field of moduli of the curve. Springer-Verlag, 2006 Sevilla David Department of Computer Science and Software Engineering, Concordia University, 1455 de Maisonneuve W., H3G 1M8, Montreal, QC, Canada aut Shaska Tanush Department of Mathematics and Statistics, Oakland University, 48309-4485, Rochester, MI, USA aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 3-20 0938-1279 18:1-2<3 2007 18 200 https://doi.org/10.1007/s00200-006-0030-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-006-0030-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sevilla David Department of Computer Science and Software Engineering, Concordia University, 1455 de Maisonneuve W., H3G 1M8, Montreal, QC, Canada aut NATIONALLICENCE 700 1- Shaska Tanush Department of Mathematics and Statistics, Oakland University, 48309-4485, Rochester, MI, USA aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 3-20 0938-1279 18:1-2<3 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer