射影多様体のgeneric initial idealと埋め込み

射影流形的一般初始理想和嵌入

• 批准号: 12740010
• 负责人: 野間 淳
• 金额: $ 1.02万
• 依托单位: Yokohama National University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-12740010/
• 关键词: projective curve; regularity; defining eguation; secant line; Castelnuovo-Mumford regularity; Projective curve

r次元射影空間の既約なd次数射影曲線Xに対する,Castelnuovo-Mumford regularityreg(X)は,定義方程式,generic initial idealの生成元の次数,ヒルベルト関数などに関係する重要姦不変量であり,本研究までに,reg(X)はd-r+2以下であることが,また上限を満たすような曲線は,非特異な有理曲線であり(d-r+2)-secant lineを持つことが知られていた.これにより、次数が十分に大きければ,reg(X)=eのとき,e-secant lineを持つことが予想されていた.本年度も引き続きこの不変量を中心にして,研究を行った.1.前年度に,曲線の算術種数p_aに対して,f:=min{P_a, r-2}とするとき,reg(X)はd-r+2-f以下であることを証明したが,今年度は,f:=r-1について考察することで,p_a≧r-1であってXが超楕円曲線でなければreg(X)はd-2r+3以下であることを証明した.これは,昨年度に得られた結果f:=r-2の次の場合に対応している.2.昨年度に,reg(X)=d-r+1となる有理曲線Xは,(d-r+1)-secant lineを持つことを証明していたが,本年度は,これをさらに精密化し,d-rが4以上で,rが4以上の場合には,Secant lineの方程式を,linear systemのsyzygyによって記述し,ただ一つしか存在しないことを証明した,これにより,埋め込みをlinear systemで与えられた有理曲線が,(d-r)-regularであるかどうかを,定義方程式を計算することなしに判定することができる.さらに,この方法によって,特別な場合の有理曲線は,極小自由分解を計算できることが解った.

R-dimensional projective space is not only the number of projective curves X, Castelnuovo-Mumford regularityreg (X), the fixed equation, the number of generators of generic initial ideal, the number of generators, the number of important variables, in this study, reg (X) is under d-r+2, and the upper limit of the curve is different. Non-specific rational curves (d-r+2)-secant line holds that you know how to make a difference. The number of times is very large, reg (X) = estranged, and e-secant line holds that you want to. This year, we will conduct a study on the number of people in the center of this year. 1. In the previous year, the number of curve arithmetic devices in the previous year, f:=min {Playa, RUV 2}, reg (X), d-r+2-f, and so on. This year, the f:=r-1 computer survey shows that there are significant differences between the two, and paar-1 shows that under the reg (X) curve, there is a clear picture of the performance of the curve. Last year, I got the results of last year. F:=r-2, I got the results. 2. Last year, reg (X) = d-r+1 rational curve X, (d-r+1)-secant line held that it was accurate and accurate, that it was accurate, that it was more than 4, that it was more than 4, that the equation was Secant line, that the linear system equation was accurate, that it was true that it was accurate, and that it was true that it did not exist. Bury the rational curve between the linear system and the regular, define the equation to calculate the equation and determine the equation. It is necessary to improve the method, especially to combine the rational curve, and to minimize the free decomposition of the calculation.

项目成果

Atushi Noma: "Gauss maps with nonthivial separable degree in positive characteristic"Journal of Pure and Applied Algebra. 156. 81-93 (2001)

Atushi Noma：“正特征中具有非零可分度的高斯映射”纯粹与应用代数杂志。

Atsushi Noma: "A bound on the Castelnuovo-Muntford regularity for curves"Mathematische Annalen. 322. 69-74 (2002)

Atsushi Noma：“曲线的 Castelnuovo-Muntford 正则性的界限”Mathematische Annalen。

Atsushi Noma: "Stability of Frobenius Pull-backs of Tangent Bundles of Weighted Complete Intersections"Mathematische Nachrichter. 221. 87-93 (2001)

Atsushi Noma：“加权完全交点切束的 Frobenius 回拉稳定性”Mathematische Nachrichter。

Atsushi Noma: "Gauss waps with nontrivial separable degree in positive characteristic"Journal of Pure and Applied Algebra. (発表予定).

Atsushi Noma：“正特征中具有非平凡可分度的高斯波”《纯粹与应用代数杂志》（待出版）。