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By Bloch S. (ed.)
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Extra info for Algebraic Geometry - Bowdoin 1985, Part 2
Bedford et al. projective spaces, we use the parametrized curve ‰ W C ! t/ D . t m 1 //. Pk /m D Pk Pk . P / . s/ 1/ / 7! s/ =x D Œy0 =x0 W W yk =xk . The exceptional hypersurfaces are given, as in the case m D 2, by J W fxj D 0g 7! ej ; : : : ; ej /. With the curve ‰, it is possible to carry through the same principle of construction as in the preceding sections. k C 1//; g, where is a cyclic permutation. The orbit length is divisible by k C 1 because the orbit of †k moves cyclically through each of the k C 1 lines.
E0 ; e0 /. As in Sect. 1; : : : ; 1; n/ with cyclic permutation (see (1)). ı kC2 k X cj ı j / C ı 2 jD0 k X cj ı j 1 jD0 D ck 1 D 2. k; n/ 2 2 then where c0 D ck D 1, and c1 D c2 D k;n is a product of cyclotomic polynomials. k; n/ 62 2 then k;n has a Salem polynomial factor and thus the largest real root is bigger than 1. 1. 3; k C 1; n 1/, so it follows that k;n is a product of cyclotomic polynomials and at most one Salem polynomial. 2, we see that the largest root of k;n increases to a Pk 1 j Pn 1 j root of ı kC2 ı k 2 jD1 ı 1 as n !
0. u C Re s; 0/ for Re s 0. -plurisubharmonic on the product of the halfplane, , with X. 2us C k 0 / 0. X; Kx CkL/ is positively curved when equipped with the metric k ks . puCk 0/ Z D ap 1 0 X eps khk2s ds C bp khk0 : (8) Since the metric on E depends only on the real part of s we can make a change of variables s D log , where is in the punctured unit disk. Abusing notation slightly we let khk D khks if s D log . pC2/ log j j khk2 d . pC2/ log j j khk2 as a singular metric defined over the whole disk, see [6, 22].