2024/11/26 by Tianqing Zhu, Zhu, Tianqing
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2411.17665
In this paper we prove the rationality of the capped vertex function with descendents for arbitrary Nakajima quiver varieties with generic stability conditions. We generalise the proof given by Smirnov to the general case, which requires to use techniques of tautological classes rather than the fixed-point basis. This result confirms that the "monodromy" of the capped vertex function is trivial, which gives a strong constraint for the monodromy of the capping operators. We will also provide a GIT wall-crossing formula for the capped vertex function in terms of the quantum difference operators and fusion operators.