By Weil A.

ISBN-10: 0387903305

ISBN-13: 9780387903309

ISBN-10: 3540903305

ISBN-13: 9783540903307

**Read Online or Download Collected papers. Vol.3 (1964-1978) PDF**

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**Extra info for Collected papers. Vol.3 (1964-1978)**

**Sample text**

Must be a normal Weierstrass point on branching in the fiber in which distinct points. 1) 0. 46 STEVEN DIAZ Step 2. 6) . 9) . of order so the generic F F a must be A . Then from the calculations in step 1 The g r °Up E aCtS b °n A then H k,B by The number of points in p Permuting H, and q R/£h which in a smooth can lie in the same fiber under two (or more) difgiven by This does not matter. more than one component at Pick n depends on whether generically two points ferent maps of points. ACA through it, the a is a generic element of some component of the labeling of the branch points.

From the Riemann singularity theorem (see for instance Kempf [1] or Griffiths and Harris [1] P. 341-342) we know that 0, if h vr (p,+*--+p 0 J) = 1 l *g-2 W . is smooth at X g-2 h (p,+-''+p _~) = h (kp-(k-g+2)q) the proof that We know and we have shown in the first paragraph of h (kp-(k-g+2)q) = 1 Before going further let us identify tangent spaces. to J(C) at any point is naturally identified with Let a) , • • •, a) be a basis for H (C,K ) some neighborhood of p, q, p,,•••>p ? The tangent space H (C,K ) * .

Deformation space l l WEIERSTRASS POINTS for the map a TT Hx C- H , and let be the subvariety of (g-k)-fold and a k-fold branch point. tf' of maps in which the the same point. of maps with both H f . 5) Let H n of 0 -> 0 C •* TT* 0 1 H Then the tangent space to at TT is -* n defined by the exact sequence. -> 0 . 6) T (HM) at . diagram. T (Hf) = H°(n f ) . ) with fibers that are generically one dimensional. Sard's theorem the differential d>. restricted to * H' will be surjective TT at every point of a generic fiber of variety of codimension one in T (H1) By $ restricted to H' • H" which meets the generic fiber of is a sub4) STEVEN DIAZ 28 restricted to H' transversely.

### Collected papers. Vol.3 (1964-1978) by Weil A.

by John

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