Wonderful compactifications and rational curves with cyclic action

Clader, Emily; Damiolini, Chiara; Li, Shiyue; Ramadas, Rohini

doi:10.1017/fms.2023.26

Cited by 2 publications

(4 citation statements)

References 29 publications

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“…One way in which to understand the special role played by the generators h S in the Chow ring of Σ π is to look more closely at the uniform case, in which case Σ π is the fan Σ r n studied in [CDLR23]. In this section, we prove that the generators h S in the uniform case are pullbacks of psi-classes under certain forgetful morphisms, analogously to the results of [DR22] for the case of Losev-Manin space.…”

Section: Intersection Numbers Of Psi-classesmentioning

confidence: 79%

“…In the special case where (E, π) is uniform with |E i | = r ≥ 2 for each i, the fan Σ π coincides with the r-permutohedral fan Σ r n studied in [CDLR23]. If, furthermore, r = 2, then it is the type-B permutohedral fan Σ Bn .…”

Section: Setmentioning

confidence: 92%

“…with relations described explicitly in Proposition 2.10. In the special case where |E i | = r for each i (in which case we refer to π as a uniform partition), the π-colored fan Σ π coincides with the fan Σ r n studied in [CDLR23], and the results of that work show that (1)…”

Section: Introductionmentioning

confidence: 92%

“…When r > 2, on the other hand, the moduli space is no longer toric, so in particular it no longer coincides with X Σ r n . Nevertheless, the main result of [CDLR23] is that L r n can be viewed as a wonderful compactification (the closure of a very affine variety) inside X Σ r n , and that the inclusion induces an isomorphism In particular, the generator x S ∈ A * (Σ r n ) restricts to the boundary divisor [X S ] ∈ A * (L r n ), which is the class of the closure of the locus X S of curves in which each spoke has length one and the light marked points on the y 0 -spoke are precisely those indexed by S. The generators h S , on the other hand, restrict to pullbacks of certain psi-classes. To explain this, we introduce the moduli space M 1 S , which parameterizes the following data:…”

Section: Intersection Numbers Of Psi-classesmentioning

confidence: 99%

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Permutohedral complexes and rational curves with cyclic action

et al. 2022

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We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids introduced by Bouchet, which naturally arise in topological graph theory. The vantage point of moduli of curves provides a tropical framework for studying multimatroids, generalizing the previous connection between type-A permutohedral varieties (Losev-Manin moduli spaces) and matroids, and the connection between type-B permutohedral varieties (Batyrev-Blume moduli spaces) and delta-matroids. Specifically, we equate a combinatorial nef cone of the moduli space with the space of R-multimatroids, a slight generalization of multimatroids, and we introduce the independence polytopal complex of a multimatroid, whose volume is identified with an intersection number on the moduli space. As an application, for the generating set of the Chow ring of the moduli space consisting of all psi-classes and their pullbacks along certain forgetful maps, we give a combinatorial formula for their intersection numbers by relating to the volumes of independence polytopal complexes of multimatroids.

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Section: Intersection Numbers Of Psi-classesmentioning

confidence: 79%

Section: Setmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 92%

Section: Intersection Numbers Of Psi-classesmentioning

confidence: 99%

See 2 more Smart Citations

Permutohedral complexes and rational curves with cyclic action

et al. 2022

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Multimatroids and Rational Curves with Cyclic Action

Clader,

Damiolini,

Eur

et al. 2024

International Mathematics Research Notices

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We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids that naturally arise in topological graph theory. The perspective of moduli of curves provides a tropical framework for studying multimatroids, generalizing the previous connection between type-$A$ permutohedral varieties (Losev–Manin moduli spaces) and matroids, and the connection between type-$B$ permutohedral varieties and delta-matroids. Specifically, we equate a combinatorial nef cone of the moduli space with the space of ${\mathbb {R}}$-multimatroids, a generalization of multimatroids, and we introduce the independence polytopal complex of a multimatroid, whose volume is identified with an intersection number on the moduli space. As an application, we give a combinatorial formula for a natural class of intersection numbers on the moduli space by relating to the volumes of independence polytopal complexes of multimatroids.

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Wonderful compactifications and rational curves with cyclic action

Cited by 2 publications

References 29 publications

Permutohedral complexes and rational curves with cyclic action

Permutohedral complexes and rational curves with cyclic action

Multimatroids and Rational Curves with Cyclic Action

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