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

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

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

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Since we are only described X t : 0. 2) Proposition. 2) > O. is all we component of I). 2). at the end of this how the proofs We will state the results section we give some brief without indications proof, of go. When we write an equation like: = ut k + ... 4) equations y2 = 4 x 3 _ r t 3 x _ s t 4, s(O) ~ 0 I~ y2 = 4 x 3 _ r t 2 x _ s t 3, r ( O ) 2 _ 2 7 s ( O ) 3 Ib(b > 0): y2 = 4x3_rx_s, I~(b > 0): y2 = 4x3_rt2x_st 3, r(O) IV C 1 (resp. or C 2) (Type IV) 2. (Type IV*) if IV*, components and C1 C3 ~ 0 ~ 0, ord A = b ~ O, s(O) and C2 ~ O, ord A = b+6.

Math. 4. On compact A. Neron: ModUles minimaux des vari6ti6s C. Schwartz: T. Shioda: S. Zucker: on normal 8. surfaces, (1983). 24, 20-59 7. analytic 78, 1-40 locaux et globaux. Pub. On generators Weierstrass On elliptic of for the W e i e r s t r a s s Math. S. of the group equation. II-III. surfaces. sur les 21 (1964). of rational Trans. , solutions to appear. J. Math. Soc. Japan (1972). Generalized functions. intermediate Inventiones J. Martin: Tate heights Math. , Soc. of sections In preparation.

Let ms be the n u m b e r one in the fiber Xs (so disc < , >~ = Idisc( Then we have: of components m s = #Gs). of multi- Then: , )NS(X)I/K ms. s Proof. 6) 0] = bi[oi-o 0] ÷ a [ F ] ÷ i>0 z where the F and C~ 1 are as in §i. I of to G-G 0 gives an isomorphism: ~ NS(×)I~[G0]~[~]+ [m[C~]). 7) [G] NS(X) (for i > 0) generated G e ~ 0 ). 5) shows that (for and H , )HI : disc< NS(X) ~ G 1 ..... ~ 0 = 0). 43)]). (evaluating which components a s section hits--its NS(X) + ~ G s. 6) we see that its kernel is preciesly H, so s that [NS(X):H] : [ ~ : ~ 0 ].

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