Commuting families in skew fields and quantization of Beauville's fibration
Commuting families in skew fields and quantization of Beauville's fibration
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斜场中的通勤家庭和博维尔纤维化的量化
DOI：
10.1215/s0012-7094-03-11921-3
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发表时间：
2001
影响因子：
2.5
通讯作者：
V. Rubtsov
中科院分区：
文献类型：
--
作者：
B. Enriquez;V. Rubtsov
在代数的对称幂的分式域上构造交换族。这个构造的经典极限给出了与线性系统相关的泊松交换族。在K3曲面S的情况下，它们对应于由Beauville引入的拉格朗日纤维化。当S是代数曲线C的标准锥时，我们构造了C的对称幂上的可交换微分算子族，量子化了Beauville系统。
We construct commuting families in fraction fields of symmetric powers of algebras. The classical limit of this construction gives Poisson commuting families associated with linear systems. In the case of a K3 surface S, they correspond to lagrangian fibrations introduced by Beauville. When S is the canonical cone of an algebraic curve C, we construct commuting families of differential operators on symmetric powers of C, quantizing the Beauville systems.