一般同调Kleiman-Bertini定理
A general homological Kleiman-Bertini theorem
摘要：
设G是作用在簇X上的光滑代数群.设F和E是X上的凝聚层。我们证明了如果F对G-轨道的所有高阶Tor层为零，则对G中的一般g，Tor^X_j（gF，E）对所有j >0为零。这推广了米勒和施派尔的结果传递群行动和结果的施派尔，本身推广了经典的克莱曼-贝尔蒂尼定理，一般横截性，在一般的群作用，光滑的子品种超过代数闭域的特征0。
英文摘要：
Let G be a smooth algebraic group acting on a variety X. Let F and E be coherent sheaves on X. We show that if all the higher Tor sheaves of F against G-orbits vanish, then for generic g in G, the sheaf Tor^X_j(gF, E) vanishes for all j >0. This generalizes a result of Miller and Speyer for transitive group actions and a result of Speiser, itself generalizing the classical Kleiman-Bertini theorem, on generic transversality, under a general group action, of smooth subvarieties over an algebraically closed field of characteristic 0.
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