By D. Burns (auth.), I. Dolgachev (eds.)
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Additional 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
S and C let ID is isomorphic to Let we may where correspond to stable curves with were contained in F(T') = @(D0) S, M r = [h e ]~ I h0(Ch,hh ) = r + 1], which intersects We claim that from the category of ~ by any neighborhood of By shrinking has normal crossing singularities at with multiplicity Now suppose ]~ scheme r + 1 = h0(£s ). hi(C,@(1)) = 0, We recall the local structure of is smooth, and In particular since contains where NOW let the points of component with C. T = [h e M r I C h Namely, satisfies be the }filbert scheme of all curves We also denote the dualizing sheaf of ¢*(~%) S 7r : X ~ S.
W@3 ® £) of degree is free on d + 3(2g - 2) ~ Let Let g M in p : C ~6 ¢*(~). ~ : S -+M so that is just ¢-l(Mr) = S r. £. Further, if Suppose Ch M is stable. Ti T T of 7r : X -+ S T Mr ~(S). (w®3 ® £), L ® w ®3 is isomorphic to *. h Let be ~ ® w ®-3. then is singular] . is equinodal~ we see at h (Cfo ). h, and locally, ~(S) k nodes. is contained in any $(S). T. eodim~ W <_ p. Let W be a component of Br which First let us define a functor D F For eacN an effective relative Cartier divisor on S XM C so that @(D) is locally isomorphici > T' to the pullback of Using Grothendieck's Quot scheme, there is an M divisor F.
Ann. 260, (1982) 317-350. : Untersuchungen ~ber Thetafunktionen, Teubner, Leipzig (1895) A CONSTRUCTION OF SPECIAL SPACE CURVES D. Gieseker* University of California Los Angeles, California 90024 §l. zero. We will work over a fixed algebraically closed field of characteristic A curve plane. i. 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 ~ .
Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981 by D. Burns (auth.), I. Dolgachev (eds.)