By Lin Weg, Iku Nakamura

Книга mathematics Geometry And quantity idea mathematics Geometry And quantity idea Книги Математика Автор: Lin Weg, Iku Nakamura Год издания: 2006 Формат: pdf Издат.:World clinical Publishing corporation Страниц: 412 Размер: thirteen ISBN: 981256814X Язык: Английский0 (голосов: zero) Оценка:Arithmetic Geometry And quantity idea (Number idea and Its Applications)By Lin Weg, Iku Nakamura

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**Additional info for Arithmetic Geometry And Number Theory**

**Example text**

R. Each Ca is 29 30 K. -K. To & L. , Ca is of type (ga, na). As such, the stable condition is equivalent to that 2ga — 2 + na > 0 for each a, that is to say, each Ca also admits the complete hyperbolic metric of constant sectional curvature —1. It is easy to see that 5ZQ=I {^9a — 3 + na) + m = Zg — Z + N. , r. 2) Weil-Petersson M e t r i c and Takhtajan-Zograf M e t r i c For any M° G Tg>jv, M° admits the complete hyperbolic metric of constant sectional curvature —1. By the uniformization theorem, M° can be represented as a quotient H\T of the upper half plane H :— {z £ C : Imz > 0} by the natural action of Fuchsian group T C PSL(2,R) of the first kind.

Since the argument for the local case is about the same as that for the global case, we omit the details here. 2 Other classical groups We also remark that there exist analogy of the above discussions for other classical groups. The functoriality from the classical groups to the general linear groups for generic representations are known through more recent work of [AS], [CKPSS04], [KK05], and [S05]. On the other hand, the analogy of the local theory for SC>2n+i in [JS03] and [JS04] is still work in progress.

S(Ci) > Os(Ci)> B = OB(Q1 + Q2 + Q3), \ = <1CI,1C 2 )B 1 Qi+Q2+Q3i where 1 denotes the defining section. In summary, if the relative dimension is 1, then for any two line bundles L\ and L2 (together with two sections si, s2 whose divisors intersect transversally) over the total space, we get a line bundle (Li, L2) (together with a section (si, s2)) on the base B in a canonical way. More generally, if TT : X —> Y is 'nice', of relative dimension n, then for any (n + 1) line bundles Lo, L i , . .