By D. Burns (auth.), I. Dolgachev (eds.)
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Extra info for Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981
J S(Zl) = z][, s(z 2) = -z 2. Step III. k(V) r is a purely transcendental extension of k, K, generated by 4 2 2 2 2 Xl' Xl/x 2' Xl/x 3' XlYl' Yl/y 2' Yl/ ' Zl(Xl+Y;)' z2(xl+Yl )" Y3 Proof. " by s s(u) = I/u: End of the proof. finally we replace x? E K, I/Y 1 4 to avoid this u by I/xlY 1 (u-l)/u+] = w In this way we have a linear action of al vector space, and with so we have equality. u = x2/ 2 = x4/ 2 2 . 1 Then but is not linear any more: eigenvalues equal to The quotient is obviously rational.
For e 40 (), g, for the situation is as follows: g ~ |0, whereas, for ([|6], [I]), g o d d ~ 25 g = 12 M ([|4J), is variety of gen- g eral type (), and D. Mumford and J. Harris announced a similar result also ii) g even the unirationality of R g for g = 5,6 has been proven only recently (, ). If the base field is of characteristic degree *) 22g - I, so that theorems A and ~2, C R is a covering of M of g g produce two rational coverings of Part of this research was done when the author was at the Institute for Advanced Study, partially supported by NSF grant MCS 81-033 65.
1. REFERENCES  P. Deligne and D. Mumford, The irreducibility genus. Publ. IHES 36 (1969), 75-109. [el J. Harris, A bound on the geometric genus of projective varieties. Norm. Sup. Pis Serie IV, vo. VII, 1 (1981), 35-68. of the space of curve of given Ann. Sci. 1] sub- sDace. submani~olds, Z, N ( M ) , a trivial of of If T*Z. X let C c M Put should space 0X c T * Z l x Now, by a paper the G r a s s m a n n of A. e. 8], fN 3, b e l o w . set of bundle of talk was motivated who worked N*(X0). complex group, of a m p l e n e s s .