Genus-zero r-spin theory

Renzo Cavalieri; Tyler Kelly; Rob Silversmith

doi:10.1112/mod.2024.2

Genus-zero r-spin theory

Renzo Cavalieri, Tyler Kelly, Rob Silversmith^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

Original language	English
Article number	e7
Number of pages	35
Journal	Moduli
Volume	1
DOIs	https://doi.org/10.1112/mod.2024.2
Publication status	Published - 29 Nov 2024

Keywords

cohomological field theory
tropical geometry
r-spin theory

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10.1112/mod.2024.2Licence: Creative Commons: Attribution (CC BY)

CavalieriR2024Genus-zeroFinal published version, 904 KBLicence: Creative Commons: Attribution (CC BY)

1 Preprint

Genus-zero r-spin theory
Cavalieri, R., Kelly, T. & Silversmith, R., 29 May 2023, arXiv.
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Open Mirror Geometry for Landau-Ginzburg Models
Kelly, T. (Principal Investigator)
Medical Research Council
1/11/20 → 31/12/24
Project: Research Councils
Bridging Frameworks via Mirror Symmetry
Kelly, T. (Principal Investigator)
Engineering & Physical Science Research Council
1/09/18 → 31/08/19
Project: Research Councils

Cite this

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title = "Genus-zero r-spin theory",

abstract = "We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.",

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author = "Renzo Cavalieri and Tyler Kelly and Rob Silversmith",

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AU - Cavalieri, Renzo

AU - Kelly, Tyler

AU - Silversmith, Rob

PY - 2024/11/29

Y1 - 2024/11/29

N2 - We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

AB - We provide an explicit formula for all primary genus-zero r-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in r. To deduce the structure of these invariants, we use a tropical realization of the corresponding cohomological field theories. We observe that the collection of all WDVV relations is equivalent to the relations deduced from the fact that genus-zero tropical CohFT cycles are balanced.

KW - cohomological field theory

KW - tropical geometry

KW - r-spin theory

U2 - 10.1112/mod.2024.2

DO - 10.1112/mod.2024.2

M3 - Article

VL - 1

JO - Moduli

JF - Moduli

M1 - e7

ER -

Genus-zero r-spin theory

Abstract

Keywords

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Fingerprint

Research output

Genus-zero r-spin theory

Projects

Open Mirror Geometry for Landau-Ginzburg Models

Bridging Frameworks via Mirror Symmetry

Cite this