Chow rings of heavy/light Hassett spaces via tropical geometry

Kannan, Siddarth; Karp, Dagan; Li, Shiyue

doi:10.1016/j.jcta.2020.105348

Cited by 5 publications

(7 citation statements)

References 15 publications

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“…Moreover, the nested set fan can be interpreted in this context as the Bergman fan of a particular matroid or as the moduli space of tropical curves. These results were generalized in [CHMR16] to all genus-zero Hassett spaces with weight system of ‘heavy/light’ type, leading to a presentation of the Chow ring of such spaces in [KKL21].…”

Section: Wonderful Compactificationsmentioning

confidence: 99%

Wonderful compactifications and rational curves with cyclic action

Clader

Damiolini

et al. 2023

Forum of Mathematics, Sigma

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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.

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Section: Wonderful Compactificationsmentioning

confidence: 99%

Wonderful compactifications and rational curves with cyclic action

Clader

Damiolini

et al. 2023

Forum of Mathematics, Sigma

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“…This procedure gives an isomorphism of Chow rings A .M 0;w / Š A .X. † 0;w //, allowing for the computation of A .M 0;w / carried out in [18].…”

Section: Related Workmentioning

confidence: 99%

“…Then we have Aut. 0;w / Š Aut.K w / Š S m S n : (1, 1, 1, 1) Heavy/light Hassett spaces are of particular interest: they are also studied in [4,10,14,18,21,22].…”

Section: Introductionmentioning

confidence: 99%

Automorphisms of tropical Hassett spaces

2022

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Given an integer g 0 and a weight vector w 2 Q n \ .0; 1 n satisfying 2g 2 C P w i > 0, let g;w denote the moduli space of n-marked, w-stable tropical curves of genus g and volume one. We calculate the automorphism group Aut. g;w / for g 1 and arbitrary w, and we calculate the group Aut. 0;w / when w is heavy/light. In both of these cases, we show that Aut. g;w / Š Aut.K w /, where K w is the abstract simplicial complex on ¹1; : : : ; nº whose faces are subsets with w-weight at most 1. We show that these groups are precisely the finite direct products of symmetric groups. The space g;w may also be identified with the dual complex of the divisor of singular curves in the algebraic Hassett space M g;w . Following the work of Massarenti and Mella (2017) on the biregular automorphism group Aut.M g;w /, we show that Aut. g;w / is naturally identified with the subgroup of automorphisms which preserve the divisor of singular curves.

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“…This space is a connected, smooth and proper Deligne-Mumford stack over Z, and is a compactification of the moduli space M 𝑔,𝑚+𝑛 of smooth pointed algebraic curves of genus g [15]; this family of weight data has been called heavy/light in the literature [7,18]. We also set M 𝑔,𝑚|𝑛 ⊂ M 𝑔,𝑚|𝑛 to be the locus of smooth, not necessarily distinctly marked curves.…”

Section: Introductionmentioning

confidence: 99%

“…where Δ 𝑔,𝑚|𝑛 is the tropical heavy/light Hassett space, studied in [7,9,19,18]. Indeed, one has 𝜒 𝑆 𝑚 ×𝑆 𝑛 (Δ 𝑔,𝑚|𝑛 ) = 𝑠 (1) 𝑚 𝑠 (2) 𝑛 − 𝐸 𝑆 𝑚 ×𝑆 𝑛 M 𝑔,𝑚|𝑛 (0, 0) when Δ 𝑔,𝑚|𝑛 is connected, which holds when 𝑔 ≥ 1, and when 𝑔 = 0 and 𝑚 + 𝑛 > 4.…”

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confidence: 99%

Equivariant Hodge polynomials of heavy/light moduli spaces

Kannan,

Serpente,

Yun

2024

Forum of Mathematics, Sigma

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Let $\overline {\mathcal {M}}_{g, m|n}$ denote Hassett’s moduli space of weighted pointed stable curves of genus g for the heavy/light weight data $$\begin{align*}\left(1^{(m)}, 1/n^{(n)}\right),\end{align*}$$ and let $\mathcal {M}_{g, m|n} \subset \overline {\mathcal {M}}_{g, m|n}$ be the locus parameterizing smooth, not necessarily distinctly marked curves. We give a change-of-variables formula which computes the generating function for $(S_m\times S_n)$ -equivariant Hodge–Deligne polynomials of these spaces in terms of the generating functions for $S_{n}$ -equivariant Hodge–Deligne polynomials of $\overline {\mathcal {M}}_{g,n}$ and $\mathcal {M}_{g,n}$ .

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Chow rings of heavy/light Hassett spaces via tropical geometry

Cited by 5 publications

References 15 publications

Wonderful compactifications and rational curves with cyclic action

Wonderful compactifications and rational curves with cyclic action

Automorphisms of tropical Hassett spaces

Equivariant Hodge polynomials of heavy/light moduli spaces

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