Project/Area Number  09640043 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  The UniversitVVy of Tokushima 
Principal Investigator 
OHBUCHI Akira University of Tokushima Associated Professor, 総合科学部, 助教授 (10211111)

CoInvestigator(Kenkyūbuntansha) 
KASHIWAGI Yoshimi Yamaguchi University Associated Professor, 経済学部, 助教授 (00152637)
TAKADA Ichiro University of Tokushima Associated Professor, 総合科学部, 助教授 (20231392)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  Curve / Code Theory / Special Divisor / 曲線 / コード理論 / 特殊線形系 / 代数曲線論 / 代数幾何学 
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 generated 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 ksheeted covering X over a curve C is shown.

Report
(4results)
Research Output
(18results)