A simplicial approach to effective divisors in M0,n

Brent Doran, Noah Giansiracusa, David Jensen

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5 Scopus citations

Abstract

We study the Cox ring and monoid of effective divisor classes of M0,n ≅= Bl ℙn-3, over a ring R. We provide a bijection between elements of the Cox ring, not divisible by any exceptional divisor section, and pure-dimensional singular simplicial complexes on {1,. ,n - 1} with weights in R \ {0} satisfying a zero-tension condition. This leads to a combinatorial criterion, satisfied by many triangulations of closed manifolds, for a divisor class to be among the minimal generators for the effective monoid. For classes obtained as the strict transform of quadrics, we present a complete classification of minimal generators, generalizing to all n the well-known Keel-Vermeire classes for n = 6.We use this classification to construct new divisors with interesting properties for all n ≥ 7.

Original languageEnglish
Pages (from-to)529-565
Number of pages37
JournalInternational Mathematics Research Notices
Volume2017
Issue number2
DOIs
StatePublished - Jan 2017

Bibliographical note

Publisher Copyright:
© The Author(s) 2016. Published by Oxford University Press. All rights reserved.0078.

ASJC Scopus subject areas

  • Mathematics (all)

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