向量丛范畴的倾斜对象

确定(2,2,n)型的权投射线的所有倾斜对象和其自同态代数。对于欧拉特征为正的其余4类权投射线，探讨从凝聚层范畴到模范畴过程中失去部分的结构。对(2,2,2,2)型的向量丛的稳定范畴的所有倾斜对象做完全分类，并确定它们的自同态代数类。对于欧拉特征为0的其余三类权投射线，我们将确定其向量丛范畴的稳定范畴的典范倾斜对象。研究对应于Arnold's strange duality的14类权投射线(欧拉特征为负)的向量层范畴的稳定范畴，确定由线丛构成的倾斜对象的自同态代数，证明其中几类与Nakayama代数导出等价的关系。从倾斜对象的突变过程理解考察Arnold奇怪对偶，并通过Ringel-Hall逼近，实现对应的这14类wild型李代数。探讨2-维Geigle-Lenzing空间的凝聚层范畴的倾斜对象以及其自同态代数。探讨一般三角范畴和导出范畴的相关基本性质。

We plan to classify all the tilting bundles in the category of coherent sheaves on a weighted projective line of weight type (2, 2, n), and investigate the abelianness of the missing part from the category of coherent sheaves to the category of modules on the associated endomorphism algebra for each tilting bundle; to describe all the tilting objects in the stable category of vector bundles on a weighted projective line of type (2, 2, 2, 2), and classify the endomorphism algebras of tilting objects in the category of coherent sheaves and in its derived category; to discuss all the tilting objects in the stable category of vector bundles on a weighted projective line of some certain weight type and the relationship with Arnold's strange duality, and try to realize the corresponding extension Lie algebras; to study some tilting objects in Geigle-Lenzing spaces.