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

(1)得到了光滑平面曲线的自同构群的一个分类。(2)对Hirzebruch曲面上的曲线的自同构群进行了分类(与Akira Ohbuhi合作)。(3)我们研究了光滑平面四次曲线的二重覆盖的weerstrass半群(与Komeda Jiryo Komeda合作)。(4)我们研究了代数曲线的平面模型的极小次数，得到了一些特殊曲线的分类(与Akira Ohbuhi合作)。(5)我们研究了含有不同不变量曲线的代数曲面上的线性系统(与加藤隆雄和Akira Obuhhi合作)。(6)我们研究了极小问题曲线在射影空间中的嵌入次数。(7)我们确定了小亏格曲线上最小次数的铅笔数(与Akira Ohbuhi合作)。

(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).