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 language | English |
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Pages (from-to) | 529-565 |
Number of pages | 37 |
Journal | International Mathematics Research Notices |
Volume | 2017 |
Issue number | 2 |
DOIs | |
State | Published - Jan 2017 |
Bibliographical note
Publisher Copyright:© The Author(s) 2016. Published by Oxford University Press. All rights reserved.0078.
ASJC Scopus subject areas
- General Mathematics