Algebraic Geometry: Summer Meeting, Copenhagen, August 7–12, by Fabrizio Catanese (auth.), Knud Lønsted (eds.)

By Fabrizio Catanese (auth.), Knud Lønsted (eds.)

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Additional info for Algebraic Geometry: Summer Meeting, Copenhagen, August 7–12, 1978

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Is a basis for coordinates k[X]and (x))=(Eai3ej) , then l 3 F6I(Y) implies Fp(aiJ)=o. I(Y) is the f(x)=(f o=F(f(x))=~Fp(aiJ)epY for be the affine closed subset of krNxk~ defined by We let Fp(XiJ)=o F6I (Y). Now k limit of FXN H. f:X+Y is given by a countable number of fi(x)£k[x]. k~xkTN={+ ÷ (aiJ)li,j6~} i d e n t i f i e d with k [q. Let for a finite n u m b e r of Let i

Schwartz: equation 3. Intersection of points 59 (1966), Jacobians math. and the t h e o r e m 33, 185-222 of abelian varieties. p. 82-110. Department Rutgers of M a t h e m a t i c s University New Brunswick, NJ (1976). 08903, USA Amer.

UI~ (z I ,.. m -nl,* = m,~ n-1 t X. y. there would exist vector fields Di~ ~ ~ m~ "Ooa, - )z~eV~ Uo~ take as local coordinates ~ so small that For ~tI < ~ D t rior o£ V1~ = ~ ( z ~ , s ~ iii), iv). is defined by (z I ..... z ~ 1 , y ~ (t)) , assume (z~ .... zk-1 ,s~ ) near and choosing conveniently $i < D~< ~2= so Vo4 = ~ (z4,s4)zi~V' ~ On D, , @ Y~. were a cobound_a such that "nj~ = m'--~"qjp (j=0,1). These equations, plus condition iv) imply that n-1 Y~ °a ~---~ = n-----~@ y ~ Y@ : being ( y ~ ) = s ~ ,~y~- ny~ ~s~ ~ This equality says that Tx in a neighbourhood of D 1-dimensional subbundle, isomorphic to 6 (D), giving on direct summand for TD.

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