Tropical Intersection Theory on Moduli Stack of Curve Coverings

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}.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2019

Author dc:creator

• Jin, Zhi

Advisor dc:contributor.advisor

• Gross, Mark

• Intersection theory
• tropical curve
• moduli stack

Licence

• https://www.repository.cam.ac.uk/bitstreams/f3274623-e965-41f5-97b6-2a96b1c891e6/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

en

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.37917

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/290718