By D. Burns (auth.), I. Dolgachev (eds.)
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Extra resources for Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981
Codim S S 3 S P. is contained L with S is Using the theory of in every component of S 3 S O - 1. Then S s But we have very ample on D, there are curves ~3 . 2 is similar to the above, except that we draw cubics through nine points of H. 0 C. l I wish to thank Joe Harris for suggesting the monodromy arguments used in this paper. §2. Let Ir : X ~ S b y some v a r i e t y nodal if all the Let ~ and suppose S. X If be a flat family of stable curves of genus s ~ S, Xs = 7 r - l ( s ) . We s a y g parametrized ~ : X ~S is equi- have the same number of nodes.
10 (1929) (reprint 1961). : The unirationality of A 5, to appear. Harris, J. 67, I(1982) 23-86. : Arithmetic variety of moduli for genus two, Annals of Math. 72(1960), 612-649. : The uniruledness of MII , to appear. : Geometric invariant theory, Springer Verlag (I~65). E. Varenna, 1969, Cremonese. : Prym varieties I, in "Contributions to Analysis", Academic Press (1974), 325-350. : La variedad de los modulos de curvas de genero 4 es unirracional, Ann. Mat. Mexicana (1971). : L'unirazionalit~ della variet~ dei moduli delle curve di genere dodici, Ann.
If smooth curves of ~enus For r = 3, be positive integers, and let (r - 1) g, ~ , d' ~ (r + 3) + g' and de~ree d' r > 3 be an integer. then there are non-degenerate i__nn ]pr. 2. curves of 5enus g' If 1 g, d' ~ and desree d' + 10, then there are non-degenerate smooth i__nn ~ . After completing this paper, I learned that Gruson and Peskine have constructed smooth curves in ~ of degree d' and genus g' g' S ~ d(d - 3) + 1. 2 is a very special case of their result. So However, their construction is quite different from the one given here.