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Some Results on Abelian Varieties
http://hdl.handle.net/10083/2065
http://hdl.handle.net/10083/2065716689d8-aec5-418f-b043-8a91c78b1589
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
KJ00004829470.pdf (802.1 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2008-04-30 | |||||
| タイトル | ||||||
| タイトル | Some Results on Abelian Varieties | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Nishi, Mieo
× Nishi, Mieo× 西, 三重雄 |
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| 著者(ヨミ) | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 69453 | |||||
| 姓名 | ニシ, ミエオ | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | The theory of divisors on an abelian variety over the field of complex numbers has been much developed by making use of the theory of theta functions. But, in the case of an abstract abelian variety, many problems are still left open. In the present paper we shall study some properties of non-degenerate divisors. First the theorem of Riemann-Roch will be stated as follows : Let X be a positive non-degenerate divisor on an abelian variety A of dimension n. Then the dimension l(X) of the complete linear system |X| is equal to (X^<(n)>)/n! and also equal to (-1)^<n+1>x_A(X), where (X^<(n)>) means the n-fold intersection number of X and x_A(X) means the virtual arithmetic genus of X. In the next place let A and B be isogenous abelian varieties and let λ be a homomorphism from A onto B. If Y is a divisor on B, then two matrices E_l(λ^<-1>(Y)) and E_l(Y) are combined by the relation E_l(λ^-(Y))=^tM_l(λ)ヅ_l(Y)ネ_l(λ), where l is a prime number different from the characteristic of our geometry. This suggests to us that, if Y is positive non-degenerate, then l(λ^<-1>(Y)) is equal to v(λ)レ(Y). Actually a proof was given under\ an additional assumption in a recent paper [4] by Morikawa. In §2 we shall show that this additional assumption can be omitted. The above equality plays an important role in the algebraic treatment of the theorem of Frobenius, and we shall discuss it in a forthcoming paper. Lastly the existence theorem of a basic polar divisor (in the sense of numerical equivalence) on a polarized abelian variety will be proved. I wish to express here my hearty thanks to Professors S. Koizumi and T. Matsusaka for their kind advices. |
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| 書誌情報 |
お茶の水女子大學自然科學報告 巻 9, 号 1, p. 1-12, 発行日 1958-07 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 00298190 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AN00033958 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 形態 | ||||||
| 802127 bytes | ||||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 400 | |||||
| 出版者 | ||||||
| 出版者 | お茶の水女子大学 | |||||
| 資源タイプ | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | 紀要論文 | |||||
| 資源タイプ・ローカル | ||||||
| 紀要論文 | ||||||
| 資源タイプ・NII | ||||||
| Departmental Bulletin Paper | ||||||
| 資源タイプ・DCMI | ||||||
| text | ||||||
| 資源タイプ・ローカル表示コード | ||||||
| 03 | ||||||
| 所属 | ||||||
| Department of Mathematics, Faculty of Science, Ochanomizu University | ||||||
