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ADJUNCTION FOR VARIETIES WITH A ℂ* ACTION
Transformation Groups ( IF 0.7 ) Pub Date : 2020-11-11 , DOI: 10.1007/s00031-020-09627-8
ELEONORA A. ROMANO , JAROSŁAW A. WIŚNIEWSKI

Let X be a complex projective manifold, L an ample line bundle on X, and assume that we have a ℂ* action on (X;L). We classify such triples (X; L;ℂ*) for which the closure of a general orbit of the ℂ* action is of degree ≤ 3 with respect to L and, in addition, the source and the sink of the action are isolated fixed points, and the ℂ* action on the normal bundle of every fixed point component has weights ±1. We treat this situation by relating it to the classical adjunction theory. As an application, we prove that contact Fano manifolds of dimension 11 and 13 are homogeneous if their group of automorphisms is reductive of rank ≥ 2.



中文翻译:

对带有ℂ*动作的变量进行调整

X为复射影流形,LX上的充足线束,并假定我们对(X ; L)具有ℂ*作用。我们对这样的三元组(X ; L ;ℂ*)进行分类,其中ℂ*动作的一般轨道相对于L的度数≤3 ,此外,该动作的源和宿是固定的点,每个固定点分量的法线束上的ℂ*作用的权重为±1。我们将这种情况与经典附加理论联系起来。作为应用,我们证明了如果尺寸为11和13的接触Fano流形的自同构群是秩≥2的约简,则它们是同质的。

更新日期:2020-11-12
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