Derived categories of irreducible projective curves of arithmetic genus one
Derived categories of irreducible projective curves of arithmetic genus one
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DOI：
10.1112/s0010437x06002090
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发表时间：
2005-03
影响因子：
1.8
通讯作者：
I. Burban;B. Kreußler
中科院分区：
文献类型：
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作者：
I. Burban;B. Kreußler
研究了算术亏格为1的不可约奇异射影曲线上凝聚层的有界导范畴。给出了该范畴的精确自等价群和所有t-结构的集合的描述。我们描述的模空间的稳定性条件，得到一个完整的分类，在这一类的所有球形物体，并表明，该组的确切的自等价作用于他们的传递。Bridgeland意义上的Harder-Narasimhan过滤被用作我们的主要技术工具。
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all $t$-structures of this category is given. We describe the moduli space of stability conditions, obtain a complete classification of all spherical objects in this category and show that the group of exact auto-equivalences acts transitively on them. Harder–Narasimhan filtrations in the sense of Bridgeland are used as our main technical tool.