The abelian/nonabelian correspondence and Frobenius manifolds, Preprint (2006), math.AG/0610265. CCLT06T.Coates,A.Corti,Y.-P.LeeandH.-H.Tseng,The quantum orbifold cohomology of weighted projective space
The abelian/nonabelian correspondence and Frobenius manifolds, Preprint (2006), math.AG/0610265. CCLT06T.Coates,A.Corti,Y.-P.LeeandH.-H.Tseng,The quantum orbifold cohomology of weighted projective space
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2006
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我们通过Frobenius流形研究了非交换商X//G的有理Gromov-Witten不变量与相应的非交换商X//T的有理Gromov-Witten不变量之间的关系(开始于[BCK2])，其中T是G中的极大环面。随后的猜想用X//T的势来表示X//G的Gromov-Witten势。当非交换商是部分旗形时，我们证明了这一猜想。
We propose an approach via Frobenius manifolds to the study (began in [BCK2]) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding " abelianized " quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds.