Thursday, 21 February 2013
Vector Bundle Model
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Pn is projective space. P1 is projective line. E is vector bundle over P1. Theorem (Grothendieck) Vector bundle E over projective line P1 is isomorphic withdirect sum of line bundles. [Note 1] Language is supposed to be projective space Pn. Word is supposed to be projective line P1. Meaning of word is supposed to be vector bundle E over projective line P1. Under the upper suppositions, by theorem (Grothendieck) meaning is identified with direct sum of line bundles. [Note 2] X is algebraic manifold. OX is module over X. L is easy sheaf of OX. Line bundle satisfies the following at L. (i) Stalk Lμ at generating point is one-dimensional vector space over functional field k(X). (ii) L is locally isomorphic with structural sheaf OX . [Note 3] (Replacement (i)) One-dimensional vector space over functional field k(X) is replaced to r-dimentional. (Replacement (ii)) Locally structural sheaf OX is replaced to to  .Replacement (i) and (ii) is called vector bundle of rank r or locally free sheaf. [Note 4] Language universal model is expressed by .[Reference] Vector bundle model is a description of the next paper of Aurora Theory. Dictoron and Aurora < Language is aurora dancing above us> For SAEKI Shizuto. Tokyo, September24, 2006. |
