1998 Fiscal Year Final Research Report Summary
| Project/Area Number |
09640043
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | The UniversitVVy of Tokushima |
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Principal Investigator |
OHBUCHI Akira University of Tokushima Associated Professor, 総合科学部, 助教授 (10211111)
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| Co-Investigator(Kenkyū-buntansha) |
TAKADA Ichiro University of Tokushima Associated Professor, 総合科学部, 助教授 (20231392)
KASHIWAGI Yoshimi Yamaguchi University Associated Professor, 経済学部, 助教授 (00152637)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Curve / Code Theory / Special Divisor |
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| Research Abstract |
1. We classify smooth projective algebraic curves C of genus g such that the variety of special linear systems W^2_(C) has dimension g - 7. We prove that W^2_(C) has dimension g - 7 <greater than or equal> 0 if and only if C is either a trigonal curve, a double cover of a curve of genus two, a curve with very ample g^3_ or a curve with g^2_.
2. We classify smooth projective algebraic curves C of genus g with normally gen-erated line bundle of degree <greater than or equal> 2g - 3. And we prove that every very ample line bundle L of degree 2g + 1 - k <less than or equal> 2g - 5 with h^1(L) = h <greater than or equal> max(2, (k - 4)/3) is normally generated, if g <greater than or equal> 6k
3. Irreducibility of W^1_(C) for d <greater than or equal> g - (k - 2) [(h+3)/] - h + 1, where C is a curve of genus g which admits an odd prime degree k map onto a general curve C of genus h > 0 is proved. Also, the existence of a component of W^1_(X) with expected dimension on a general k-sheeted covering X over a curve C is shown.
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