Nonexistence of semiorthogonal decompositions and sections of the canonical bundle

Nonexistence of semiorthogonal decompositions and sections of the canonical bundle
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不存在半正交分解和正则丛的截面

DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Shinnosuke Okawa
Shinnosuke Okawa
中科院分区：
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文献类型：
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作者：
Kotaro Kawatani;Shinnosuke Okawa

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研究了光滑真簇上凝聚层导出范畴的半正交分解。我们证明了全球/局部部分的规范丛给一个强约束的支持对象的半正交和。我们还表明，SODs是刚性的拓扑平凡的自等价的作用下。作为这些结果的应用，我们证明了各种极小模型的非平凡SOD的不存在性。
We investigate semiorthogonal decomposition(SOD)s of the derived category of coherent sheaves on a smooth proper variety. We prove that global/local sections of the canonical bundle give a strong constraint on the supports of objects in one of the semiorthogonal summands. We also show that SODs are rigid under the action of topologically trivial autoequivalences. As applications of these results, we prove the non-existence of non-trivial SODs for various minimal models.