88
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Enumerating Hassett’s Wall and Chamber Decomposition of the Moduli Space of Weighted Stable Curves

, , &
Pages 36-53 | Published online: 20 Feb 2018
 

ABSTRACT

Hassett constructed a class of modular compactifications of Mg,n by adding weights to the marked points. This leads to a natural wall and chamber decomposition of the domain of admissible weights Dg,n, where the moduli space and universal family remain constant inside a chamber, and may change upon crossing a wall. The goal of this paper is to count the number of chambers in this decomposition. We relate these chambers to a class of boolean functions known as linear threshold functions (LTFs), and discover a subclass of LTFs which are in bijection with the chambers. Using this relation, we prove an asymptotic formula for the number of chambers, and compute the exact number of chambers for n ⩽ 9. In addition, we provide an algorithm for the enumeration of chambers of Dg,n and prove results in computational complexity.

2000 AMS SUBJECT CLASSIFICATION:

Acknowledgments

We thank Dori Bejleri, Patricio Gallardo, Brendan Hassett, Dave Jensen, Steffen Marcus, Sam Payne, and Dhruv Ranganathan for helpful discussions and suggestions. We thank Nicolle Gruzling for providing us with code used to enumerate linear threshold functions for n ⩽ 9. Finally, we thank the referee for many usual suggestions that helped improve this paper.

Additional information

Funding

This research was completed as part of the SUMRY (Summer Undergraduate Mathematics Research at Yale) program during the summer of 2017, where the first author was a mentor and the other authors were participants. SUMRY is supported in part by NSF Grant CAREER DMS-1149054. K.A. was supported in part by an NSF Postdoctoral Fellowship.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 360.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.