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ABSTRACT: We construct for any smooth projective curve of genus $q\ge 2$ with a fixed point free automorphism a nonisotrivial family of curves. Moreover we study the space of modular curves and that of parameters. Comment: 13 pages.A not expected logo of Transaction of Ams has accidentally appeared on the first page for a few days (till 14 September when they noticed the logo and they removed it). So it has been withdrawn in sign of respect towards Transaction of Ams and Le Matematiche of Catania where the paper has been sent
09/2005;