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Wonderful compactifications and rational curves with cyclic action

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Abstract We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane… Click to show full abstract

Abstract We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces. By proving a general result on such wonderful compactifications, we conclude that this moduli space is Chow-equivalent to an explicit toric variety (whose fan can be understood as a tropical version of the moduli space), from which a computation of its Chow ring follows.

Keywords: wonderful compactifications; moduli space; cyclic action; rational curves; curves cyclic

Journal Title: Forum of Mathematics, Sigma
Year Published: 2022

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