Symplectic resolutions for nilpotent orbits
Symplectic resolutions for nilpotent orbits
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DOI：
10.1007/s00222-002-0260-9
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发表时间：
2002-05
影响因子：
3.1
通讯作者：
Baohua Fu
中科院分区：
文献类型：
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作者：
Baohua Fu
本文首先计算了经典复单李代数中幂零轨道π的Picard群，讨论了π的闭包的正规化π的阶乘和阶乘性质。然后我们考虑带符号的辛分解问题。𝒪我们的主要定理是，对于半单复李代数中的任何幂零轨道π，如果对于分解π：Z π π（ω），定义在π−1（π）上的2-形式π*（ω）扩张到Z上的辛2-形式，则Z同构于射影齐性空间的余切轨道T *（G/P），π是零截面的坍缩。证明了Cho-Miyaoka-Shepherd-Barron的一个猜想。利用这个定理，我们确定所有品种的等压线;其中承认这样的决议。
In this paper, firstly we calculate Picard groups of a nilpotent orbit 𝒪 in a classical complex simple Lie algebra and discuss the properties of being ℚ-factorial and factorial for the normalization 𝒪tilde; of the closure of 𝒪. Then we consider the problem of symplectic resolutions for 𝒪tilde;. Our main theorem says that for any nilpotent orbit 𝒪 in a semi-simple complex Lie algebra, equipped with the Kostant-Kirillov symplectic form ω, if for a resolution π:Z𝒪tilde;, the 2-form π*(ω) defined on π−1(𝒪) extends to a symplectic 2-form onZ, thenZis isomorphic to the cotangent bundleT*(G/P) of a projective homogeneous space, and π is the collapsing of the zero section. It proves a conjecture of Cho-Miyaoka-Shepherd-Barron in this special case. Using this theorem, we determine all varieties 𝒪tilde; which admit such a resolution.