Chow rings of heavy/light Hassett spaces via tropical geometry

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Kannan, Siddarth¹  Karp, Dagan²  Li, Shiyue¹ 

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

[2] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

关键词: Tropical geometry;    Moduli spaces of curves;    Matroid;    Chow ring;   

DOI  :  10.1016/j.jcta.2020.105348

来源: Elsevier

【 摘 要 】

We compute the Chow ring of an arbitrary heavy/light Hassett space (M) over bar (0,w). These spaces are moduli spaces of weighted pointed stable rational curves, where the associated weight vector w consists of only heavy and light weights. Work of Cavalieri et al. [3] exhibits these spaces as tropical compactifications of hyperplane arrangement complements. The computation of the Chow ring then reduces to intersection theory on the toric variety of the Bergman fan of a graphic matroid. Keel [16] has calculated the Chow ring A* ((M) over bar (0,n)) of the moduli space (M) over bar (0,n) of stable nodal n-marked rational curves; his presentation is in terms of divisor classes of stable trees of P-1's having one nodal singularity. Our presentation of the ideal of relations for the Chow ring A*((M) over bar (0,w)) is analogous. We show that pulling back under Hassett's birational reduction morphism rho(w): (M) over bar (0,n) -> (M) over bar (0,w) identifies the Chow ring A* ((M) over bar (0,w)) with the subring of A * ((M) over bar (0,n)) generated by divisors of w-stable trees, which are those trees which remain stable in (M) over bar (0,w). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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