## Tropical Intersection Theory on Moduli Stack of Curve Coverings

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##### Authors

Jin, Zhi

##### Advisors

Gross, Mark

##### Date

2019-06-01##### Awarding Institution

University of Cambridge

##### Author Affiliation

Pure Mathematics and Mathematical Statistics

##### Qualification

Doctor of Philosophy (PhD)

##### Language

English

##### Type

Thesis

##### Metadata

Show full item record##### Citation

Jin, Z. (2019). Tropical Intersection Theory on Moduli Stack of Curve Coverings (Doctoral thesis). https://doi.org/10.17863/CAM.37917

##### Abstract

We construct the moduli cone stack $\mathfrac{M}_\eta^\text{trop}$ of tropical \'{e}tale covers (i.e., coverings of twisted tropical curves). We define the tropical intersection theory on $\mathfrac{M}_\eta^\text{trop}$ and show that the tropical intersection theory agrees with the intersection theory on the moduli stack $\bar{\mathfrac{M}}_\eta$ of \'{e}tale covers (i.e., coverings of twisted algebraic curves). We apply the tropical intersection theory on $\mathfrac{M}_\eta^\text{trop}$ to calculate the intersection numbers of Psi-classes on the moduli space $\bar{\mathfrac{M}}_{g,n}$ of $n$-marked genus $g$ curves. We also define the moduli stack $\mathfrac{M}_\eta^\text{log}$ of logarithmic \'{e}tale covers and describe the tropicalization map from $\mathfrac{M}_\eta^\text{log}$ to the Artin fan of $\mathfrac{M}_\eta^\text{trop}$.

##### Keywords

Intersection theory, tropical curve, moduli stack

##### Identifiers

This record's DOI: https://doi.org/10.17863/CAM.37917

##### Rights

All rights reserved