1989 Fiscal Year Final Research Report Summary
Structure of Algebraic Varieties
| Project/Area Number |
63540035
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
TAKEMOTO Fumio Nagoya Inst. Technol., Engineering, Assistant Professor, 教育学部, 助教授 (90024033)
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| Co-Investigator(Kenkyū-buntansha) |
竹内 義浩 愛知教育大学, 教育学部, 助手 (10206956)
石戸谷 公直 愛知教育大学, 教育学部, 助教授 (80133130)
YAMAZATO Makoto Nagoya Inst. Technol., Engineering, Assistant Professor (00015900)
ADACHI Toshiaki Nagoya Inst. Technol., Engineering, Instructor (60191855)
YAMADA Hiroshi Nagoya Inst. Technol., Engineering, Professor (20022551)
KATO Akikuni Nagoya Inst. Technol., Engineering, Assistant Professor (20024226)
IWASHITA Hirokazu Nagoya Inst. Technol., Engineering, Instructor (30193741)
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| Project Period (FY) |
1987 – 1989
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| Keywords | Class of Algebraic Surfaces / Criterion of Ruled Surfaces / Classification of Algebraic Surfaces / ex-ホモトピ-論 / ファイバ-的トポロジ- / ファイバ-的ホモトピ- / ホワイトヘッド積 |
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| Research Abstract |
Let S ( P^n be a non-singular projective complex algebraic surface of degree d and class m. We can prove the following propositions. PROPOSITION 1. (1) Let m <less than or equal> d+19. Then S is ruled. (2) Let m = d+20. Then either (a) S is ruled, or (b) n = 4 and S is an abelian surface. PROPOSITION 2. (1) Let m <less than or equal> 2d+9. Then S is ruled. (2) Let m 2d+10. Then either (a) S is ruled, or (b) m = d+20. To prove the above propositions, we need the next proposition. This is a solution of the problem proposed by Livorni. PROPOSITION 3. (1) Let S be a hyperelliptic surface. Then n <double plus> 4. (2) Let S be a minimal elliptic surface. Assume d = 9 , the sectional genus 6 and chi( O_S ) = 0. Then n = 3. Other results taken by investigators are stated in articles whose titles we put on next page
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Research Products
(15 results)
