Research for Morse theory and module maps of degenerate familios of curves

摩尔斯理论与简并曲线族模图研究

• 批准号: 12640037
• 负责人: ASHIKAGA Tadashi
• 金额: $ 0.83万
• 依托单位: Tohoku-Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 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/grant/KAKENHI-PROJECT-12640037/
• 关键词: degeneration; morsification; family of curves; atomic fiber; signature; monodromy; hyperlliptic curre; semi-stable reduction; Morsification; splitting family; Horikawa index; modali map; atomic fiber; degeneration; monodromy; stable curve

We continued the study of the Modification problem of degenerate families of hyperelliptic curves with Tatsuya Arakawa. We obtained the results about the certain obstruction for the existence of hyperelliptic splitting families, the classification of hyperelliptic atomic fibers of genus 3 and so on. We wrote the paper with him entitled "Local splitting families of hyperelliptic pencils, II". (The part I of this series was already published, see "REFERENCES".)Based on the recent studies of myself and Kazuhiro Konno, we wrote the survey paper with him about the results and open problems in the field of global and local studies of pencils of algebraic curves, see "REFERENCES".We obtained the certain formula of the signature defect of degeneration of curves, which comes from the semi-stable reduction of the family. This is an application of the G-signature theorem of Atiyah-Singer. We are now trying to develop this study, and will publish it in near future.

我们与Tatsuya Arakawa一起继续研究了超椭圆曲线退化族的修正问题。得到了超椭圆分裂科存在的一定阻碍、超椭圆原子纤维3属的分类等结果。我们和他一起写了一篇题为“超椭圆铅笔的局部分裂家族，II”的论文。（本系列的第一部分已经发表，请参阅“参考资料”。）基于我和Kazuhiro Konno最近的研究，我们与他一起撰写了关于代数曲线铅笔的全球和本地研究领域的结果和开放问题的调查论文，见参考文献。从族的半稳定约简得到了曲线退化的特征缺陷的确定公式。这是Atiyah-Singer的g签名定理的一个应用。我们正在努力发展这项研究，并将在不久的将来发表。

项目成果

T. Arakawa and T. Ashikaga: "Local splitting families of hyperlliptic pencils, I"Tohoku Math. J.. 53. 369-394 (2001)

T.荒川和T.足利：“超椭圆铅笔的局部分裂家族，我”东北数学。

T.Ashikaga, K.Konno: "Global and local properties of pencils of algebraic curves"Proceedings of the conference "algebraic geometry Azumino 2000". (印刷中). (2002)

T.Ashikaga、K.Konno：“代数曲线铅笔的全局和局部性质”会议论文集“代数几何 Azumino 2000”（印刷中）。

T.Ashikaga, M.Ishizaka: "Classification of degenerations of curves of genus three via Matsumoto-montesions theorem"Tohoku Math. J.. 54(印刷中). (2002)

T.Ashikaga、M.Ishizaka：“通过 Matsumoto-montesions 定理对三格曲线的退化进行分类”Tohoku Math J.. 54（出版中）。

T. Ashikaga and K. Konno: "Global and local prooerties of pencils of algebraic curves"to appear in Procedings of the conference "Algebraic geomethy Azumino. (2000)

T. Ashikaga 和 K. Konno：“代数曲线铅笔的全局和局部性质”出现在“代数几何安昙野”会议记录中。(2000)

T.Arakawa, T.Ashikaga: "Local splitting families of hyperelliptic pencils, I"Tohoku Math. J.. 53. 369-394 (2001)

T.Arakawa，T.Ashikaga：“超椭圆铅笔的局部分裂家族，我”东北数学。