研究权型大于等于4的权投射线上向量丛范畴的稳定范畴，确定并构造稳定范畴中的倾斜对象；刻画椭圆曲线与亏格为1的权投射线之间的关系，进一步探讨椭圆曲线上的向量丛范畴能否成为Frobenius范畴；将代数表示论中热门的研究对象generic模、Pruefer模及adic模推广到椭圆曲线以及亏格小于等于1的权投射线的拟凝聚层范畴中，考察这些对象在凝聚层范畴的分类中所起的作用，并利用这些对象来构造拟凝聚层范畴中的倾斜对象与余倾斜对象。以上研究，涉及代数几何、代数表示论，奇异理论和幂零算子理论等几个数学分支，是权投射线及椭圆曲线上的拟凝聚层范畴理论的新探索，也是学科交叉前沿的进一步探索。

Study the stable category of vector bundles on the weighted projective lines of type greater than or equal to 4, determine whether they contain tilting objects, and then construct tilting objects for those who contain; describe the relationship between elliptic curves and the weighted projective lines of genus 1, and then discuss whether the category of vector bundles on an elliptic curve can become a Frobenius category; extend the notions of generic modules, Pruefer modules and adic modules to the category of quasi-coherent sheaves on the elliptic curves and the weighted projective lines of genus less than or equal to 1, observe the role played by these objects in the classification of the coherent sheaves category, and then construct tilting objects and cotilting objects over the category of quasi-coherent sheaves. The above studies involve algebraic geometry, algebraic representation theory, singularity theory and nilpotent operator theory, and several other study fields of mathematics. It is not only new exploration to the category of quasi-coherent sheaves on projective lines and elliptic curves, but also the further exploration of the interdisciplinary study.