A study of linear systems on algebraic curves and its application for varieties of general type

(1)给出了光滑平面曲线的自同构群的分类。(2)我们分类的自同构群曲线Hirzebruch表面（联合工作与Akira Ohbuchi）。(3)我们研究了光滑平面四次线的双重覆盖的Weierstrass半群（与Jiryo Komeda的联合工作）。(4)我们研究了代数曲线平面模型的最小次数，并得到了一些特殊曲线的分类（与Akira Ohbuchi的联合工作）。(5)我们研究了代数曲面上的线性系统，其中包含具有不同不变量的曲线（与Takao Kato和Akira Ohbuchi的联合工作）。(6)研究了曲线在射影空间中嵌入的最小次数。(7)我们确定了小亏格曲线上最小程度的铅笔数（与Akira Ohbuchi的联合工作）。

(1) We obtained a classification of automorphism groups of smooth plane curves.(2) We classified automorphism groups of curves on Hirzebruch surfaces (joint work with Akira Ohbuchi).(3) We studied Weierstrass semigroups of double coverings of smooth plane quartics (joint work with Jiryo Komeda).(4) We studied the minimal degree of plane models of algebraic curves and obtained a classification of some special curves (joint work with Akira Ohbuchi).(5) We studied linear systems on algebraic surfaces containing curves with different invariants (joint work with Takao Kato and Akira Ohbuchi).(6) We studied the minimal degree of embeddings of curves into projec tive spaces.(7) We determined the number of pencils of minimal degree on curves of small genus (joint work with Akira Ohbuchi).